Practice the problems of Math in Focus Grade 7 Workbook Answer Key Chapter 4 Lesson 4.4 Solving Algebraic Inequalities to score better marks in the exam.

## Math in Focus Grade 7 Course 2 A Chapter 4 Lesson 4.4 Answer Key Solving Algebraic Inequalities

### Math in Focus Grade 7 Chapter 4 Lesson 4.4 Guided Practice Answer Key

**Copy and complete. Solve each inequality and graph the solution set on a number line.**

Question 1.

0.2x + 3 + 0.8x ≤ 4

0.2x + 3 + 0.8x ≤ 4

+ 3 ≤ 4 Add the like terms.

+ 3 ≤ 4 – Subtract from both sides.

≤ Simplify.

Answer:

**x ≤ 1**

Explanation:

Given, 0.2x + 3 + 0.8x ≤ 4

x + 3 ≤ 4

Subtract 3 on both sides.

x + 3 – 3 ≤ 4 – 3

x ≤ 1

Question 2.

\(\frac{1}{4}\)x – 1 + \(\frac{3}{4}\)x > 0

\(\frac{1}{4}\)x – 1 + \(\frac{3}{4}\)x > 0

– 1 > 0 Add the like terms.

– 1 + > 0 + Add to both sides.

> Simplify.

Answer:

**x > 1**

Explanation:

Given, (1/4)x – 1 + (3/4)x >0

x – 1 > 0

Add 1 on both sides.

x – 1 + 1 > 0 + 1

x > 1

**Solve each inequality and graph the solution set on a number line.**

Question 3.

2x + 3 < 13 + x

Answer:

**x < 10**

Explanation:

Given, 2x + 3 < 13 + x

Subtract x and 3 on both sides.

2x + 3 – x – 3 < 13 + x – x – 3

x < 10

Question 4.

1.5x – 3 ≥ 4 + 0.5x

Answer:

**x ≥ 7**

Explanation:

Given, 1.5x – 3 ≥ 4 + 0.5x

Subtract 0.5x o both sides.

1.5x – 3 – 0.5x ≥ 4 + 0.5x – 0.5x

1x – 3 ≥ 4

Add 3 on both sides.

x – 3 + 3 ≥ 4 + 3

x ≥ 7

Question 5.

4 + \(\frac{1}{3}\)x > 8 + \(\frac{4}{3}\)x

Answer:

**x < 4**

Explanation:

Given, 4 + (1/3)x > 8 + (4/3)x

Subtract (1/3)x on both sides.

4 + (1/3)x – (1/3)x > 8 + (4/3)x – (1/3)x

4 > 8 -x

Subtract 8 on both sides.

4 – 8 > 8 -x – 8

-x < -4

x < 4

**Hands-On Activity**

EXPLORE DIVISION AND MULTIPLICATIVE PROPERTIES OF AN INEQUALITY

Work individually.

Step 1: Use a copy of this table. Complete each using the symbols > or <.

**Math Journal** What happens to the direction of the inequality symbol when you divide by a positive number? Based on your observation, write a rule for dividing both sides of an inequality by a positive number.

**Math Journal** What happens to the direction of the inequality symbol when you divide by a negative number? Based on your observation, write a rule for dividing both sides of an inequality by a negative number.

Step 2: Use a copy of this table. Complete each using the symbols > or <.

**Math Journal** What happens to the direction of the inequality symbol when you multiply by a positive number? Based on your observation, write a rule for multiplying both sides of an inequality by a positive number.

**Math Journal** What happens to the direction of the inequality symbol when you multiply by a negative number? Based on your observation, write a rule for multiplying both sides of an inequality by a negative number.

**Solve each inequality and graph the solution set on a number line.**

Question 6.

–\(\frac{1}{5}\)w ≤ 2

Answer:

**x ≥ -10**

Explanation:

Given, -(1/5)x ≤ 2

Multiply 5 on both sides

-(1/5)x × 5 ≤ 2 × 5

-x ≤ 10

x ≥ -10

Question 7.

-7m > 21

Answer:

**m < -3**

Explanation:

Given, -7m > 21

Divide 7 on both sides.

-7m ÷ 7 > 21 ÷ 7

-m > 3

m < -3

Question 8.

6 > -0.3y

Answer:

y > -20

Explanation:

Given, 6 > -0.3y

Divide 0.3 on both sides.

6 ÷ 0.3 > -0.3y ÷ 0.3

20 > -y

y > -20

**Solve each inequality and graph the solution set on a number line.**

Question 9.

4y + 7 < 27

4y + 7 < 27

4y + 7 – < 27 – Subtract from both sides.

4y < Simplify.

4y ÷ < ÷ Divide both sides by .

y < Simplify.

Answer:

**y < 5**

Explanation:

Given, 4y + 7 < 27

Subtract 7 on both sides.

4y + 7 – 7 < 27 – 7

4y < 20

Divide 4 on both sides

4y ÷ 4 < 20 ÷ 4

y < 5

Question 10.

-5y – 9 > 21

-5y – 9 > 21

-5y – 9 + ≥ 21 + Add to both sides.

-5y ≥ Simplify.

– 5y ÷ ≤ ÷ Divide both sides by and reverse the inequality symbol.

y ≤ Simplify.

Answer:

**y ≤ -6**

Explanation:

Given, -5y – 9 > 21

Add 9 on both sides.

-5y – 9 + 9 > 21 + 9

– 5y > 30

Divide 5 on both sides.

– 5y ÷ 5 > 30 ÷ 5

-y < 6

y ≤-6

Question 11.

\(\frac{1}{2}\)x + \(\frac{3}{4}\) ≥ 5

Answer:

**x ≥ (17/2)**

Explanation:

Given, (1/2)x + (3/4) ≥ 5

Subtract (3/4) on both sides.

(1/2)x + (3/4) – (3/4) ≥ 5 – (3/4)

(1/2)x ≥ (20 – 3)/4

(1/2)x ≥ (17/4)

Multiply 2 on both sides

(1/2)x × 2 ≥ (17/4) × 2

x ≥ (17/2)

Question 12.

1.5 – 0.3y > 3.6

Answer:

**y < -7**

Explanation:

Given, 1.5 – 0.3y > 3.6

Subtract 1.5 on both sides.

1.5 – 0.3y – 1.5 > 3.6 – 1.5

-0.3y > 2.1

Divide -0.3 on both sides

-0.3y ÷ (-0.3) > 2.1 ÷ (-0.3)

y < -7

Question 13.

-8y + 32 ≤ -17 – y

Answer:

**y ≥ 7**

Explanation:

Given, -8y + 32 ≤ -17 – y

Add y on both sides

-8y + 32 + y ≤ -17 – y + y

-7y +32 ≤ -17

Subtract 32 on both sides.

-7y +32 – 32 ≤ -17 -32

-7y ≤ -49

Divide -7 on both sides.

-7y ÷ (-7) ≤ -49 ÷ (-7)

y ≥ 7

Question 14.

4(2 – y) ≥ 20

Answer:

**y ≤ -3**

Explanation:

Given, 4(2 – y) ≥ 20

8 – 4y ≥ 20

Subtract 8 on both sides

8 – 4y – 8 ≥ 20 – 8

-4y ≥ 12

Divide -4 on both sides

-4y ÷ (-4) ≥ 12 ÷ (-4)

y ≤ -3

### Math in Focus Course 2A Practice 4.4 Answer Key

**Solve each inequality using addition and subtraction. Then graph each solution set on a number line.**

Question 1.

x + 8 > 14

Answer:

**x > 6**

Explanation:

Given, x + 8 > 14

Subtract 8 on both sides.

x + 8 – 8 > 14 – 8

x > 6

Question 2.

2 ≥ x – 12

Answer:

**x ≤14**

Explanation:

Given, 2 ≥ x – 12

Add 12 on both sides.

2 + 12 ≥ x – 12 + 12

14 ≥ x

x ≤14

Question 3.

-7x + 5 + 8x > 3

Answer:

**x > -2**

Explanation:

Given, -7x + 5 + 8x > 3

x + 5 > 3

Subtract 5 on both sides.

x + 5 – 5 > 3 – 5

x > -2

Question 4.

– 2x – 3 + 3x ≥ 12

Answer:

**x ≥ 15**

Explanation:

Given, -2x – 3 + 3x ≥ 12

x – 3 ≥ 12

Add 3 on both sides.

x – 3 + 3 ≥ 12 + 3

x ≥ 15

Question 5.

29 < \(\frac{2}{3}\)x + 14 + \(\frac{1}{3}\)x

Answer:

**x>15**

Explanation:

29 < (2/3)x + 14 + (1/3)x

Subtract 14 on both sides.

29 – 14 < (2/3)x + 14 + (1/3)x – 14

15 < x

x>15

Question 6.

\(\frac{1}{5}\)x + 9 + \(\frac{4}{5}\)x > -11

Answer:

**x > -20**

Explanation:

Given, (1/5)x + 9 + (4/5)x > -11

Subtract 9 on both sides.

(1/5)x + 9 + (4/5)x – 9 > -11 – 9

x > -20

Question 7.

0.7x + 4 + 0.3x ≤ 10

Answer:

**x ≤ 6**

Explanation:

Given, 0.7x + 4 + 0.3x ≤ 10

Subtract 4 on both sides.

0.7x + 4 + 0.3x – 4 ≤ 10 – 4

x ≤ 6

Question 8.

0.4x – 6 + 0.6x ≥ 19

Answer:

**x ≥ 25**

Explanation:

Given , 0.4x – 6 + 0.6x ≥ 19

x – 6 ≥ 19

Add 6 on both sides.

x – 6 + 6 ≥ 19 + 6

x ≥ 25

Question 9.

3x + 4 < 2x + 9

Answer:

**x < 5**

Explanation:

Given, 3x + 4 < 2x + 9

Subtract 4 on both sides.

3x + 4 – 4 < 2x + 9 – 4

3x < 2x + 5

Subtract 2x on both sides

3x – 2x < 2x + 5 – 2x

x < 5

Question 10.

8 – 4x > 12 – 3x

Answer:

**x < -4**

Explanation:

Given, 8 – 4x > 12 – 3x

Add 3x on both sides

8 – 4x + 3x > 12 – 3x +3x

8 -x > 12

Subtract 8 on both sides.

8 -x – 8 > 12 – 8

-x > 4

x < -4

Question 11.

\(\frac{2}{3}\)x + 2 ≥ 9 – \(\frac{1}{3}\)x

Answer:

**x ≥ 7**

Explanation:

Given, (2/3)x + 2 ≥ 9 – (1/3)x

Add (1/3)x on both sides

(2/3)x + 2 + (1/3)x ≥ 9 – (1/3)x + (1/3)x

x +2 ≥ 9

Subtract 2 on both sides.

x +2 – 2 ≥ 9 – 2

x ≥ 7

Question 12.

13 + 1\(\frac{3}{5}\)x ≥ 18 + \(\frac{3}{5}\)x

Answer:

**x ≥ 5**

Explanation:

Given, 13 + 1(3/5)x ≥ 18 + (3/5)x

13 + (8/5)x ≥ 18 + (3/5)x

Subtract (3/5)x on both sides.

13 + (8/5)x – (3/5)x ≥ 18 + (3/5)x – (3/5)x

13 + x ≥ 18

Subtract 13 on both sides.

13 + x – 13 ≥ 18 – 13

x ≥ 5

Question 13.

1.7x + 5 < 16 + 0.7x

Answer:

**x < 11**

Explanation:

Given, 1.7x + 5 < 16 + 0.7x

Subtract 0.7x on both sides.

1.7x + 5 – 0.7x < 16 + 0.7x – 0.7x

5 + x < 16

Subtract 5 on both sides.

5 + x – 5 < 16 – 5

x < 11

Question 14.

8.5 – 0.9x > 9.8 – 1.9x

Answer:

**x < 1.3**

Explanation:

Given, 8.5 – 0.9x > 9.8 – 1.9x

Add 0.9x on both sides.

8.5 – 0.9x + 0.9x > 9.8 – 1.9x + 0.9x

8.5 > 9.8 – x

Subtract 9.8 on both sides.

8.5 – 9.8 > 9.8 – x – 9.8

-1 .3 > – x

x < 1.3

Question 15.

**Math Journal** Solve the inequality 8 + 2x ≥ 12 and show your work. What value is a solution of 8 + 2x ≥ 12 but is not a solution of 8 + 2x > 12?

Answer:

x ≥ 2, x > 2 Both the solutions are not same.

Explanation:

Given, two equations: 8 + 2x ≥ 12

8 + 2x > 12

Let us solve 1st equation: 8 + 2x ≥ 12

Subtract 8 on both sides.

8 + 2x – 8 ≥ 12 – 8

2x ≥ 4

Divide 2 on both sides

2x ÷ 2 ≥ 4 ÷ 2

x ≥ 2

Let us solve 2nd equation:

8 + 2x > 12

Subtract 8 on both sides.

8 + 2x – 8 > 12 – 8

2x > 4

Divide 2 on both sides

2x ÷ 2 > 4 ÷ 2

x > 2

Question 16.

**Math Journal** Eric solved the inequality 6y ≤ -18 as shown below:

6y ≤ -18

6y ÷ 6 ≥ -18 ÷ 6

y ≥ -3

Describe and correct the error that Eric made.

Answer:

**y ≥ 3**

Explanation:

Given, 6y ≤ -18

Divide 6 on both sides.

6y ÷ 6 ≥ -18 ÷ 6

y ≥ 3

**Solve each inequality using division and multiplication. Then graph the solution set on a number line.**

Question 17.

3 ≥ -3x

Answer:

**x ≥ -1**

Explanation:

Given, 3 ≥ -3x

Divide 3 on both sides.

3 ÷ 3 ≥ -3x ÷ 3

1 ≥ -x

x ≥ -1

Question 18.

-4x > 12

Answer:

**x < -3**

Explanation:

Given, -4x > 12

Divide -4 on both sides.

-4x ÷ – 4 > 12 ÷ – 4

x < -3

Question 19.

–\(\frac{x}{5}\) ≤ 2

Answer:

**x ≥ -10**

Explanation:

Given, -(x/5) ≤ 2

Multiply -5 on both sides.

-(x/5) ≤ 2

-(x/5) × -5 ≤ 2 × -5

x ≥ -10

Question 20.

–\(\frac{2}{3}\)x > 8

Answer:

**x < -12**

Explanation:

Given, -(2/3)x > 8

Multiply 3 on both sides.

-(2/3)x × 3 > 8 × 3

-2x > 24

Divide -2 on both sides.

-2x ÷ -2 > 24 ÷ -2

x < -12

Question 21.

-0.2x ≥ 6

Answer:

**x ≤ -30**

Explanation:

Given, -0.2x ≥ 6

Divide -0.2 on both sides.

-0.2x ÷ -0.2 ≥ 6 ÷ -0.2

x ≤ -30

Question 22.

9 > -0.5x

Answer:

**x > – 18**

Explanation:

Given, 9 > -0.5x

Divide – 0.5 on both sides.

9 ÷ -0.5 > -0.5x ÷ -0.5

-18 >x

x > – 18

**Solve each inequality using the four operations. Then graph each solution set on a number line.**

Question 23.

7y – 3 > 11

Answer:

**y > 2**

Explanation:

Given, 7y – 3 > 11

Add 3 on both sides.

7y – 3 + 3 > 11 + 3

7y > 14

Divide 7 on both sides.

7y ÷ 7 > 14 ÷ 7

y > 2

Question 24.

-3a + 5 < -7

Answer:

**a > 4**

Explanation:

Given, -3a + 5 < -7

Subtract 5 on both sides.

-3a + 5 – 5 < -7 – 5

-3a < -12

Divide -3 on both sides.

-3a ÷ -3 < -12 ÷ -3

a > 4

Question 25.

\(\frac{x}{4}\) + \(\frac{3}{16}\) ≥ 1

Answer:

**x ≥ (13/4)**

Explanation:

(x/4) + (3/16) ≥ 1

multiply 4 on both sides.

((x/4) + (3/16) ) × 4 ≥ 1 × 4

x + (3/4) ≥ 4

Subtract (3/4) on both sides.

x + (3/4) – (3/4) ≥ 4 – (3/4)

x ≥ (13/4)

Question 26.

\(\frac{3}{5}\)a – \(\frac{4}{5}\) < \(\frac{7}{10}\)

Answer:

**a < (5/2)**

Explanation:

Given, (3/5)a – (4/5) < (7/10)

Add (4/5) on both sides.

(3/5)a – (4/5) + (4/5) < (7/10) + (4/5)

(3/5)a < ((7+(4 × 2))/10)

(3/5)a < (7+8)/10

(3/5)a < 15/10

Divide 3 on both sides.

(3/5)a ÷ 3 < 15/10 ÷ 3

(a/5) < (5/10)

(a/5) < (1/2)

Multiply 5 on both sides.

(a/5) × 5 < (1/2) × 5

a < (5/2)

Question 27.

7 – 0.3x > 4

Answer:

**x < 10**

Explanation:

Given, 7 – 0.3x > 4

Subtract 7 on both sides.

7 – 0.3x – 7 > 4 – 7

-0.3x > -3

Divide -0.3 on both sides.

-0.3x ÷ -0.3 > -3 ÷ -0.3

x < 10

Question 28.

2.4y + 5 < 29

Answer:

**y < 10**

Explanation:

Given, 2.4y + 5 < 29

Subtract 5 on both sides.

2.4y + 5 – 5 < 29 – 5

2.4y < 24

Divide 2.4 on both sidea.

2.4y ÷ 2.4 < 24 ÷ 2.4

y < 10

Question 29.

5x + 3 < 7 + 7x

Answer:

**x > -2**

Explanation:

Given, 5x + 3 < 7 + 7x

Subtract 3 on both sides.

5x + 3 – 3 < 7 + 7x – 3

5x < 4 + 7x

subtract 5x on both sides.

5x -5x < 4 + 7x – 5x

0 < 4 + 2x

-4 < 2x

2x > -4

Divide 2 on both sides.

2x ÷ 2 > -4 ÷ 2

x > -2

Question 30.

11 – 7x ≤ 20 – 8x

Answer:

**x ≤ 9**

Explanation:

Given, 11 – 7x ≤ 20 – 8x

Subtract 11 on both sides.

11 – 7x – 11 ≤ 20 – 8x – 11

-7x ≤ 9 – 8x

8x – 7x ≤ 9

x ≤ 9

Question 31.

\(\frac{4}{3}\) – \(\frac{5}{6}\)x ≥ –\(\frac{1}{6}\) – \(\frac{2}{3}\)x

Answer:

**x ≤ 7**

Explanation:

Given, (4/3) – (5/6)x ≥ -(1/6) – (2/3)x

Add (2/3)x on both sides.

(4/3) – (5/6)x + (2/3)x ≥ -(1/6) – (2/3)x + (2/3)x

(4/3) – ((5x – 4x)/6) ≥ -(1/6)

(4/3) -(x/6) ≥ -(1/6)

Add (1/6) on both sides.

(4/3) -(x/6) + (1/6) ≥ -(1/6) + (1/6)

((6 + 1)/6) – x/6 ≥ 0

(7/6) – x/6 ≥ 0

7 – x ≥ 0

7 ≥ x

x ≤ 7

Question 32.

\(\frac{2}{5}\)x + 4 ≤ \(\frac{7}{10}\)x – 8

Answer:

**x ≥ 40**

Explanation:

Given, (2/5)x + 4 ≤ (7/10)x – 8

Subtract 4 on both sides.

(2/5)x + 4 – 4 ≤ (7/10)x – 8 – 4

(2/5)x ≤ (7/10)x – 12

12 ≤ (7/10)x – (2/5)x

12 ≤ (7 – 4)x/10

12 ≤ 3x/10

Multiply 10 on both sides.

12 × 10 ≤ 3x/10 × 10

120 ≤ 3x

Divide 3 on both sides.

120 ÷ 3 ≤ 3x ÷ 3

40 ≤ x

x ≥ 40

Question 33.

5.4x + 4.2 – 3.8x > 9

Answer:

**x > 3**

Explanation:

Given, 5.4x + 4.2 – 3.8x > 9

1.6x + 4.2 > 9

Subtract 4.2 on both sides.

1.6x + 4.2 – 4.2 > 9 – 4.2

1.6x > 4.8

Divide 1.6 on both sides.

1.6x > 4.8

1.6x ÷ 1.6 > 4.8 ÷ 1.6

x > 3

Question 34.

6.6 + 1.3x – 5.2x ≤ 14

Answer:

Explanation:

Given, 6.6 + 1.3x – 5.2x ≤ 14

Subtract 6.6 on both sides.

6.6 + 1.3x – 5.2x – 6.6 ≤ 14 – 6.6

-3.9x ≤ 7.4

Divide -3.9 on both sides.

-3.9x ÷ -3.9 ≤ 7.4 ÷ -3.9

x ≥ -(74/39)

**Solve each inequality with parentheses using the four operations.**

Question 35.

3(y + 2) ≤ 18

Answer:

**y ≤ 4**

Explanation:

Given, 3(y + 2) ≤ 18

Divide 3 on the both sides.

3(y + 2) ÷ 3 ≤ 18 ÷ 3

(y + 2) ≤ 6

Subtract 2 on both sides.

y + 2 – 2 ≤ 6 – 2

y ≤ 4

Question 36.

8(y – 1) > 24

Answer:

**y > 4**

Explanation:

Given, 8(y – 1) > 24

Divide 8 on both sides.

8(y – 1) ÷ 8 > 24 ÷ 8

y – 1 > 3

Add 1 on both sides.

y – 1 + 1 > 3 + 1

y > 4

Question 37.

\(\frac{1}{2}\)(a + 1) ≤ 4

Answer:

**a ≤ 7**

Explanation:

Given, (1/2) (a + 1) ≤ 4

Multiply 2 on both sides.

(1/2) (a + 1) × 2 ≤ 4 × 2

a +1 ≤ 8

Subtract 1 on both sides.

a +1 -1 ≤ 8 – 1

a ≤ 7

Question 38.

\(\frac{2}{3}\)(3 – a) < 3

Answer:

**a > -(3/2)**

Explanation:

Given, (2/3)(3 – a) < 3

Divide (2/3) on both sides.

(2/3)(3 – a) ÷ (2/3) < 3 ÷ (2/3)

(3 – a) < (9/2)

Subtract 3 on both sides.

3 – a – 3 < (9/2) – 3

-a < (9-6)/2

a > -(3/2)

Question 39.

1.3(2 – x) > 3.9

Answer:

**x < -1**

Explanation:

Given, 1.3(2 – x) > 3.9

Divide 1.3 on both sides.

1.3(2 – x) ÷ 1.3 > 3.9 ÷ 1.3

2 – x > 3

Subtract 2 on both sides.

2 – x – 2 > 3 – 2

-x > 1

x < -1

Question 40.

3.6(5x – 1) < 5.4

Answer:

**x < (1/2)**

Explanation:

Given, 3.6(5x – 1) < 5.4

Divide 3.6 on both sides.

3.6(5x – 1) ÷ 3.6 < 5.4 ÷ 3.6

5x -1 < 1.5

Add 1 on both sides.

5x -1 + 1 < 1.5 + 1

5x < 2.5

Divide 5 on both sides.

5x ÷ 5 < 2.5 ÷ 5

x < (1/2)

Question 41.

4 + 2(1 – 3y) < 36

Answer:

**y > -5**

Explanation:

Given, 4 + 2(1 – 3y) < 36

Subtract 4 on both sides.

4 + 2(1 – 3y) – 4 < 36 – 4

2(1 – 3y) < 32

Divide 2 on both sides.

2(1 – 3y) ÷ 2 < 32 ÷ 2

1 – 3y < 16

Subtract 1 on both sides.

1 – 3y – 1 < 16 – 1

-3y < 15

Divide -3 on both sides.

-3y ÷ -3 < 15 ÷ -3

y > -5

Question 42.

2(3 – x) > 5x – 1

Answer:

**x < 1**

Explanation:

Given, 2(3 – x) > 5x – 1

6 – 2x > 5x – 1

Add 1 on both sides.

6 – 2x + 1 > 5x – 1 + 1

7 -2x > 5x

Add 2x on both sides.

7 -2x + 2x > 5x + 2x

7 > 7x

Divide 7 on both sides.

7 ÷ 7 > 7x ÷ 7

1 > x

x < 1

Question 43.

\(\frac{5}{9}\)(x + 1) ≥ \(\frac{2}{3}\)

Answer:

**x ≥ (1/5)**

Explanation:

Given, (5/9)(x + 1) ≥ (2/3)

Multiply 9 on both sides.

(5/9)(x + 1) × 9 ≥ (2/3) × 9

5 (x + 1) ≥ 2 × 3

5 (x + 1) ≥ 6

Divide 5 on both sides.

5 (x + 1) ÷ 5 ≥ 6 ÷ 5

x + 1 ≥ (6/5)

Subtract 1 on both sides.

x + 1 – 1 ≥ (6/5) – 1

x ≥ (6-5)/5

x ≥ (1/5)

Question 44.

\(\frac{2}{3}\)(1 – 3x) > \(\frac{1}{6}\)

Answer:

**x < (1/4)**

Explanation:

Given, (2/3) (1 – 3x) > (1/6)

Multiply 3 on both sides.

(2/3) (1 – 3x) × 3 > (1/6) × 3

2 (1 – 3x) > (1/2)

Divide 2 on both sides.

2 (1 – 3x) ÷ 2 > (1/2) ÷ 2

1 – 3x > (1/4)

Subtract 1 on both sides.

1 – 3x – 1 > (1/4) – 1

-3x > -(3/4)

Divide -3 on both sides.

-3x ÷ -3 > -(3/4) ÷ -3

x < (1/4)

Question 45.

1.7 + 0.2(1 – x) ≥ 2.7

Answer:

**x ≤ -4**

Explanation:

Given, 1.7 + 0.2(1 – x) ≥ 2.7

1.7 + 0.2 -0.2x ≥ 2.7

1.9 – 0.2x ≥ 2.7

Subtract 1.9 on both sides.

1.9 – 0.2x – 1.9 ≥ 2.7 – 1.9

-0.2x ≥ 0.8

Divide -0.2 on both sides.

-0.2x ÷ -0.2 ≥ 0.8 ÷ -0.2

x ≤ -4

Question 46.

2.5(3 – 2x) + 1 ≥ 29

Answer:

**x ≤ 4.1**

Explanation:

Given, 2.5(3 – 2x) + 1 ≥ 29

7.5 – 5x + 1 ≥ 29

8.5 -5x ≥ 29

Subtract 8.5 on both sides.

8.5 -5x – 8.5 ≥ 29 – 8.5

-5x ≥ 20.5

Divide -5 on both sides.

-5x ÷ -5 ≥ 20.5 ÷ -5

x ≤ 4.1

Question 47.

**Math Journal** Compare solving the inequality -5(x + 6) < 10 with solving the equation -5(x + 6) = 10. Describe the similarities and differences between solving the inequality and solving the equation. Explain how the solution set of the inequality -5(x + 6) < 10 is different from the solution of the equation -5(x + 6) = 10.

Answer:

The solution of the equation -5(x + 6) < 10 is x > -8, which represents the number x can be any number greater than -8.

The solution of the equation -5(x + 6) = 10 is x = -8, here the number x will be only -8 not any other number.

Explanation:

Given two equations are, -5(x + 6) < 10 and -5(x + 6) = 10

Let us consider -5(x + 6) < 10

Divide -5 on both sides.

-5(x + 6) ÷ -5 < 10 ÷ -5

(x + 6) > -2

Subtract 6 on both sides.

x + 6 – 6 > -2 – 6

x > -8

Let us consider the second equation -5(x + 6) = 10

Divide -5 on both sides.

-5(x + 6) ÷ -5 = 10 ÷ -5

(x + 6) = -2

Subtract 6 on both sides.

x + 6 – 6 = -2 – 6

x = -8

**Solve each inequality using the four operations.**

Question 48.

10 – 3(4a – 3) < 2(3a – 4) – 9.2

Answer:

**a > 2.01**

Explanation:

Given, 10 – 3(4a – 3) < 2(3a – 4) – 9.2

10 – 12a + 9 < 6a – 8 – 9.2

19 – 12a < 6a – 17.2

Subtract 6a on both sides.

19 – 12a – 6a < 6a – 17.2 – 6a

19 – 18a < -17.2

Subtract 19 on both sides.

19 – 18a – 19 < -17.2 – 19

-18a <-36.2

Divide -18 on both sides.

-18a ÷ -18 <-36.2 ÷ -18

a > 2.01

Question 49.

7(2a – 3) ≤ 5 – 2(3a – 1)

Answer:

**a ≤ (7/5)**

Explanation:

Given, 7(2a – 3) ≤ 5 – 2(3a – 1)

14a – 21 ≤ 5 – 6a + 2

14a -21 ≤ 7 – 6a

Subtract 7 on both sides.

14a -21 – 7 ≤ 7 – 6a – 7

14a -28 ≤ -6a

Add 6a on both sides.

14a -28 + 6a ≤ -6a + 6a

20a ≤ 28

Divide 20 on both sides.

20a ÷ 20 ≤ 28 ÷ 20

a ≤ (7/5)