# Math in Focus Grade 7 Chapter 4 Lesson 4.2 Answer Key Solving Algebraic Equations

Practice the problems of Math in Focus Grade 7 Workbook Answer Key Chapter 4 Lesson 4.2 Solving Algebraic Equations to score better marks in the exam.

## Math in Focus Grade 7 Course 2 A Chapter 4 Lesson 4.2 Answer Key Solving Algebraic Equations

### Math in Focus Grade 7 Chapter 4 Lesson 4.2 Guided Practice Answer Key.

Solve.

Question 1.
6x + 2 = 8
6x + 2 = 8
6x + 2 – = 8 – Subtract from both sides. = Simplify.
$$\frac{?}{?} x=\frac{?}{?}$$ Divide both sides by .
x = Simplify.
x =1

Explanation:
6x+2 =8

Subtract 2 on both sides.

6x + 2 – 2 = 8 -2

6x = 6

x =1

Let us consider second question, $$\frac{?}{?} x=\frac{?}{?}$$

Let us consider, a and b in the place of the “?” on both sides

(a/b)x = (a/b)

Divide (a/b) on both sides.

x =1

Question 2.
5 – 3x = 20
x = -5

Explanation:
Let us consider the equation,   5 – 3x = 20

Subtract 5 both sides.

5 – 3x – 5 = 20 – 5

-3x = 15

put  – on both sides to make x positive.

-(-3x) = -15

3x = -15

divide 3 on both sides to get the value of ‘x’

x = -5

Question 3.
4x – 3 + 0.5x = 1.5
x = 1

Explanation:
4x – 3 + 0.5x = 1.5

Add all the variants of ‘x’

4.5x – 3 = 1.5

4.5x -3 + 3 = 1.5 + 3

4.5x = 4.5

divide 4.5 on both sides.

x= (4.5/4.5)

x = 1

Question 4.
$$\frac{9}{10}$$x – $$\frac{4}{5}$$ = 1
x = 2

Explanation:
(9/10)x – (4/5) = 1

(9/10)x – (4/5) + (4/5) = 1 + (4/5)

(9/10)x = (9/5)

0.9x =  1.8

Divide (0.9) on both sides.

x = 1.8 ÷ 0.9

x = 2

Solve each equation. Check your solution.

Question 5.
11 – 4x = x + 16
11 – 4x = x + 16
11 – 4x – x = x + 16 – x Subtract x from both sides.
11 + = 16 Simplify.
11 + – 11 = 16 – 11 Subtract 11 from both sides = 5 Simplify.
$$\frac{?}{?} x=\frac{?}{?}$$ Divide both sides by .
x = Simplify.
-5x = 5

Explanation:
Given, 11 – 4x = x + 16

Subtract x from both sides.

11 – 4x – x = x + 16 – x

11 – 5x =16

Subtract 11 from both sides.

11 – 5x – 11=16 – 11

-5x = 5

x = -1

Let us consider second question, $$\frac{?}{?} x=\frac{?}{?}$$

Let us consider, a and b in the place of the “?” on both sides

(a/b)x = (a/b)

Substitute -1 in the place of  x

(a/b)(-1) = (a/b)

Divide (a/b) on both sides.

= -1

Question 6.
3.4y – 5.2 = 3y + 2
y = 18

Explanation:
Given, 3.4y – 5.2 = 3y + 2

(34/10)y – (52/10) = 3y + 2

Simplify (34/10) and (52/10), and bring 3y + 2 to another side.

(17/5)y – 26/5 – 3y – 2 = 0

get common divider to all.

17y – 26 – 5.(3y + 2) / 5 = 0

(17y – 26 – 15y – 10) / 5  = 0

(2y – 36 )/ 5 = 0

(2y – 36 ) = 0 × 5

2y – 36 = 0

2y = 36

y = 18

Question 7.
$$\frac{5}{9}$$y – $$\frac{1}{3}$$ = $$\frac{2}{3}$$y + $$\frac{1}{3}$$
y= -6

Explanation:
Given, (5/9)y – (1/3) = (2/3)y + (1/3)

(5/9)y – (1/3) + (1/3)= (2/3)y + (1/3) + (1/3)

(5/9)y = (2/3)y + (2/3)

(5/9)y – (2/3)y = (2/3)

(5y – 3×2y)/9 = (2/3)

(5y – 6y)/9 = (2/3)

-y = (2/3) × 9

-y = 6

y= -6

Solve each equation. Check your solutions.

Question 8.
1.5(p + 3) = 18
p = 9

Explanation:
Given, 1.5(p + 3) = 18

It can also be written as 1.5p + 4.5 = 18

Subtract 4.5 on both sides

1.5p + 4.5 – 4.5 = 18 -4.5

1.5p = 13.5

Divide 1.5 on both sides.

1.5p ÷ 1.5 =  13.5 ÷ 1.5

p = 9

Question 9.
$$\frac{1}{4}$$(q+ 1) = 9
q = 35

Explanation:
Given, (1/4)(q + 1) = 9

multiply 4 on both sides.

(q + 1) = 36

Subtract 1 on both sides.

q +1 – 1 = 36 – 1

q = 35

Question 10.
2(x – 3) + 2 = 14
x =9

Explanation:
Given, 2(x – 3) + 2 = 14

2x – 6 + 2 = 14

2x – 4 = 14

2x – 4 + 4 = 14 + 4

2x = 18

x =9

Question 11.
3(y – 1) + y = 1
y =1

Explanation:
Given, 3(y – 1) + y = 1

3y – 3 + y = 1

4y – 3 = 1

Add 3 on the both sides

4y – 3 + 3 =1 + 3

4y = 4

y =1

### Math in Focus Course 2A Practice 4.2 Answer Key

Solve each equation with variables on the same side.

Question 1.
4b – 2 = 6
b = 2

Explanation:
Given, 4b – 2 = 6

Add 2 on the both sides.

4b – 2 + 2 = 6 + 2

4b = 8

b = 8 ÷ 4

b = 2

Question 2.
5x + 4 = 24
x = 4

Explanation:
Given, 5x + 4 = 24

Subtract 4 on both sides.

5x + 4 – 4 = 24

5x = 20

Divide 5 on both sides

x = 20 ÷ 5

x = 4

Question 3.
7c – 11 = 17
c = 4

Explanation:
Given, 7c – 11 = 17

7c – 11 + 11 = 17 +11

7c = 28

Divide 7 on bot sides.

c =  28 ÷ 7

c = 4

Question 4.
18 = 3k – 3
7 = k

Explanation:
Given, 18 = 3k – 3

18 + 3 = 3k – 3 + 3

21 = 3K

Divide 3 on both sides.

21 ÷ 3 = 3k ÷ 3

7 = k

Question 5.
$$\frac{a}{4}$$ – 1 = 3
a = 16

Explanation:
Given, (a/4) -1 = 3

(a/4) -1 + 1 = 3 + 1

(a/4) = 4

Multiply 4 on both sides.

(a/4) × 4 = 4 × 4

a = 16

Question 6.
$$\frac{2}{3}$$v = 2 – $$\frac{4}{3}$$
v =1

Explanation:
Given, (2/3)v = 2 – (4/3)

(2/3)v = (2×3 -4)/3

(2/3)v = (6 – 4)/3

(2/3)v = (2/3)

Multiply (3/2) on both sides.

(2/3)v ×(3/2) = (2/3) ×(3/2)

v =1

Question 7.
$$\frac{5}{2}$$y + 8 =18
y = 4

Explanation:
(5/2)y + 8 = 18

Subtract 8 on both sides.

(5/2)y + 8 – 8 = 18 – 8

(5/2)y = 10

Multiply 2 on both sides.

(5/2)y × 2 = 10 × 2

5y = 20

Divide 5 on both sides.

5y ÷ 5 = 20 ÷ 5

y = 4

Question 8.

$$\frac{3}{5}$$f – $$\frac{1}{2}$$ = $$\frac{1}{2}$$
f = (5/3)

Explanation:
Given, (3/5)f – (1/2) = (1/2)

(3/5)f – (1/2) + (1/2) = (1/2) + (1/2)

(3/5)f = 1

Multiply 5 on both sides.

(3/5)f  × 5 = 1 × 5

3f = 5

Divide 3 on both sides.

f = (5/3)

Question 9.
4.5 + 0.2p = 6.1
p = 8

Explanation:
Given, 4.5 + 0.2p = 6.1

Subtract 4.5 on both sides.

4.5 + 0.2p – 4.5 = 6.1 – 4.5

0.2p = 1.6

Divide 0.2 on both sides.

0.2p ÷ 0.2 = 1.6 ÷ 0.2

p = 8

Question 10.
1.5d + 3.2 = 9.2
d = 4

Explanation:
Given, 1.5d + 3.2 = 9.2

Subtract 3.2 on both sides.

1.5d + 3.2 – 3.2  = 9.2 – 3.2

1.5d = 6

Divide 1.5 on both sides.

1.5d  ÷ 1.5 = 6 ÷ 1.5

d = 4

Question 11.
0.8w – 4 = 4
w = 10

Explanation:
Given, 0.8w – 4 = 4

0.8w – 4 + 4 = 4 + 4

0.8w =8

Divide 0.8 on both sides.

0.8w ÷ 0.8 =8 ÷ 0.8

w = 10

Question 12.
1.4z – 0.5 = 3.7
z = 3

Explanation:
Given, 1.4z – 0.5 = 3.7

1.4z – 0.5 + 0.5 = 3.7 + 0.5

1.4z = 4.2

Divide 1.4 on both sides.

1.4z ÷ 1.4 = 4.2 ÷ 1.4

z = 3

Question 13.
Math Journal Priscilla was asked to solve the equation -4p + 5 = 7. Her solution is shown. Priscilla concluded that p = $$\frac{1}{2}$$ is the solution of the equation -4p + 5 = 7. Describe and correct the error Priscilla made.
The answer priscilla got is wrong. P = – (1/2)

Explanation:
Given,-4p + 5 = 7

Subtract 5 on both sides.

-4p + 5 – 5= 7 – 5

-4p = 2

Divide 4 on both sides

-p = (2/4)

p = – (1/2)

Solve each equation with variables on both sides.

Question 14.
6a + 7 = 4a + 7
a = 0

Explanation:
Given, 6a + 7 = 4a + 7

Subtract 7 on both sides.

6a + 7 – 7 = 4a + 7 – 7

6a = 4a

6a -4a = 0

2a = 0

a = 0

Question 15.
17g + 3 = 11g + 39
g = 6

Explanation:
Given, 17g + 3 = 11g + 39

17g + 3 – 11g – 39 = 0

6 g – 36 = 0

6g = 36

Divide 6 on both sides.

6g ÷ 6 = 36 ÷ 6

g = 6

Question 16.
8h – 5 = 11h – 14
h = 3

Explanation:
Given, 8h – 5 = 11h – 14

14 – 5 = 11h – 8h

9 = 3h

Divide 3 on both sides.

3h ÷ 3 = 9 ÷ 3

h = 3

Question 17.
9j + 4 = 13j – 6
j = (5/2)

Explanation:
Given, 9j + 4 = 13j – 6

4 + 6 = 13j – 9j

10 =  4j

Divide 4 on both sides.

j = (10/4)

j = (5/2)

Question 18.
$$\frac{1}{2}$$f – 2 = $$\frac{1}{6}$$f
f = 6

Explanation:
Given, (1/2)f – 2 = (1/6)f

(1/2)f – (1/6)f = 2

(3f – f)/6 = 2

Multiply  6 on both sides.

2f = 2 × 6

2f = 12

Divide 2 on both sides.

f = 12 ÷ 2

f = 6

Question 19.
25 + q = $$\frac{1}{2}$$q – 3
q = -56

Explanation:
Given, 25 + q = (1/2)q – 3

25 + 3 = (1/2)q – q

28 = -(1/2)q

Multiply 2 on both sides.

28 × 2 = -(1/2)q × 2

-q = 56

q = -56

Question 20.
$$\frac{5}{9}$$v – $$\frac{1}{3}$$ = $$\frac{2}{3}$$v + $$\frac{1}{3}$$
v = -6

Explanation:
Given, (5/9)v – (1/3) = (2/3)v + (1/3)

(5/9)v – (1/3) + (1/3) = (2/3)v + (1/3) + (1/3)

(5/9)v = (2/3)v + (2/3)

Subtract (2/3)v on both sides.

(5/9)v – (2/3)v = (2/3)v + (2/3) – (2/3)v

(5v – 6v)/9 = (2/3)

-v = (2/3) × 9

-v = 2 × 3

-v =6

v = -6

Question 21.
$$\frac{5}{4}$$e + $$\frac{1}{2}$$ = 2e – $$\frac{1}{2}$$
e = (4/3)

Explanation:
Given, (5/4)e + (1/2) = 2e – (1/2)

(5/4)e + (1/2) + (1/2) = 2e – (1/2) + (1/2)

(5/4)e + 1 = 2e

1 = 2e – (5/4)e

1 = ((2 × 4)e -5e)/4

(8e – 5e)/4 = 1

(3e/4) = 1

Multiply 4 on both sides.

(3e/4) × 4 = 1 × 4

3e = 4

e = (4/3)

Question 22.
7.5x – 4.1 = 6.7 – 4.5x
x = 0.9

Explanation:
Given, 7.5x – 4.1 = 6.7 – 4.5x

7.5x – 4.1 + 4.1 = 6.7 – 4.5x + 4.1

7.5x = 10.8 – 4.5x

7.5x + 4.5x = 10.8 – 4.5x + 4.5x

12x =10.8

x = (10.8/12)

x = 0.9

Question 23.
3.4y – 5.2 = 3y + 2
y = 18

Explanation:
Given, 3.4y – 5.2 = 3y + 2

Subtract 2 on both sides.

3.4y – 5.2  – 2 = 3y + 2 – 2

3.4y -7.2 = 3y

3.4y – 3y = 7.2

0.4y = 7.2

Divide 0.4 on both sides.

0.4y ÷ 0.4 = 7.2 ÷ 0.4

y = 18

Question 24.
b – 2.8 = 0.8b + 1.2
b = 20

Explanation:
Given, b – 2.8 = 0.8b + 1.2

Subtract 1.2 on both sides.

b – 2.8 – 1.2 = 0.8b + 1.2 – 1.2

b – 4 = 0.8b

b – 0.8b = 4

0.2b = 4

Divide 0.2 on both sides.

0.2b ÷ 0.2 = 4 ÷ 0.2

b = 20

Question 25.
3.2s – 5 = 5 – 1.8s
s =2

Explanation:
Given, 3.2s – 5 = 5 – 1.8s

3.2s – 5 + 5 = 5 – 1.8s + 5

3.2s = 10 – 1.8s

3.2s + 1.8s = 10 – 1.8s + 1.8s

5s = 10

Divide 5 on both sides.

5s ÷ 5 = 10 ÷ 5

s =2

Question 26.
Math Journal How is the process of solving the equation $$\frac{3}{5}$$x – 1 = $$\frac{3}{10}$$x + $$\frac{1}{5}$$ different from simplifying the expression $$\frac{3}{5}$$x – 1 + $$\frac{3}{10}$$ x + $$\frac{1}{5}$$?
x = 4, (9x -8)/10  Yes both are different from each other.

Explanation:
Given equations, (3/5)x – 1 = (3/10)x + (1/5)

(3/5)x -1 + (3/10)x + (1/5)

Let’s solve the first equation, (3/5)x – 1 = (3/10)x + (1/5)

Subtract (1/5) on both sides.

(3/5)x – 1 – (1/5) = (3/10)x + (1/5) – (1/5)

(3/5)x -(5 + 1)/5 = (3/10)x

(3/5)x – (6/5) = (3/10)x

(3/5)x – (3/10)x = (6/5)

(6 – 3)x/10 = (6/5)

Multiply 10 on both sides.

3x/10 × 10 = (6/5) × 10

3x = 12

Divide 3 on both sides

3x ÷ 3 = 12 ÷ 3

x = 4

Lets solve second equation, (3/5)x -1 + (3/10)x + (1/5)

(6 + 3)x/10 – 1 + (1/5)

9x/10 -(4/5)

(9x -8)/10

Solve each equation involving parentheses.

Question 27.
7(2z + 1) = 35
z =2

Explanation:
Given, 7(2z + 1) = 35

Divide 7 on both sides.

7(2z + 1) ÷  7 = 35 ÷ 7

2z + 1 = 5

Subtract 1 on both sides

2z + 1 – 1 = 5 – 1

2z = 4

z =2

Question 28.
18 = 6(5 – g)
g = 2

Explanation:
Given, 18 = 6(5 – g)

18 = 30 – 6g

6g = 30 -18

6g = 12

Divide 6 on both sides.

6g ÷ 6 = 12 ÷ 6

g = 2

Question 29.
$$\frac{1}{5}$$(3r – 4) = $$\frac{2}{5}$$
r = 2

Explanation:
(1/5)(3r – 4) = (2/5)

Multiply 5 on both sides.

(1/5)(3r – 4)  × 5 = (2/5) × 5

(3r – 4) = 2

3r – 4 + 4 = 2 + 4

3r = 6

Divide 3 on both sides.

3r ÷ 3 = 6 ÷ 3

r = 2

Question 30.
$$\frac{1}{5}$$(5x + 4) = $$\frac{3}{4}$$
x = -(1/20)

Explanation:
(1/5)(5x + 4) = (3/4)

Multiply 5 on both sides.

(1/5)(5x + 4) = (3/4)

(1/5)(5x + 4) × 5 = (3/4) × 5

(5x + 4) = (15/4)

Multiply 4 on both sides.

(5x + 4) × 4 = (15/4) × 4

20x + 16 = 15

Subtract 16 on both sides.

20x + 16 – 16 = 15 -16

20x = -1

Divide 20 on both sides.

20x ÷ 20 = -1 ÷ 20

x = -(1/20)

Question 31.
0.6(d + 3) = 3d
d = 0.75

Explanation:
Given, 0.6(d + 3) = 3d

0.6d + 1.8 = 3d

Subtract 1.8 on both sides.

0.6d + 1.8 – 1.8= 3d – 1.8

0.6d = 3d – 1.8

3d – 0.6d = 1.8

2.4d ÷  2.4 = 1.8 ÷ 2.4

d = 0.75

Divide 2.4 on both sides.

2.4d = 1.8

Question 32.
0.3(k – 0.2) = 0.6
k = 2.2

Explanation:
Given, 0.3(k – 0.2) = 0.6

Divide 0.3 on both sides.

0.3(k – 0.2) ÷ 0.3 = 0.6 ÷ 0.3

k – 0.2 = 2

k – 0.2 + 0.2 = 2 + 0.2

k = 2.2

Question 33.
3(1.2b – 1) + 3.6 = 4.2
b = 1

Explanation:
Given, 3(1.2b – 1) + 3.6 = 4.2

3.6b – 3 + 3.6 = 4.2

3.6b + 0.6 = 4.2

Subtract 0.6 on both sides.

3.6b + 0.6 – 0.6 = 4.2 -0.6

3.6b = 3.6

Divide 3.6 on both sides.

3.6b ÷ 3.6 = 3.6 ÷ 3.6

b = 1

Question 34.
0.7(h + 2) + 1.6 = 17
h = 20

Explanation:
Given, 0.7(h + 2) + 1.6 = 17

0.7h + (0.7 × 2) + 1.6 = 17

0.7h + 1.4 + 1.6 = 17

0.7h + 3 = 17

Subtract 3 on both sides.

0.7h + 3 – 3 = 17 – 3

0.7h = 14

Divide 0.7 on both sides.

0.7h ÷ 0.7 = 14 ÷ 0.7

h = 20

Question 35.
2(a – 1) – 5a = 7

Explanation:
Given, 2(a – 1) – 5a = 7

2a -2 -5a = 7

-3a – 2 = 7

Add 2 on the both sides.

-3a – 2+2 = 7 +2

-3a = 9

Divide -3 on both sides.

a = -(9/3)

a = -3

Question 36.
3(6 – 4x) – 27x = 10x – 31
1 = x

Explanation:
Given, 3(6 – 4x) – 27x = 10x – 31

18 – 12x – 27x = 10x -31

18 -39x = 10x – 31

18 +31 = 10x + 39x

49 = 49x

Divide 49 on both sides.

49 ÷ 49 = 49x ÷ 49

1 = x

Question 37.
$$\frac{1}{4}$$(w – 4) – $$\frac{3}{4}$$w = 3
w = -8

Explanation:
Given, (1/4)(w – 4) – (3/4)w =3

Multiply 4 on both sides.

4 ×( (1/4)(w – 4) – (3/4)w) = 3 × 4

(w – 4) – 3w = 12

w – 4 – 3w = 12

-2w – 4 = 12

-2w – 4 + 4 = 12 + 4

-2w = 16

-w = 8

w = -8

Question 38.
$$\frac{1}{6}$$s – $$\frac{1}{2}$$(s – 2) = $$\frac{45}{2}$$
s = -(129/2)

Explanation:
(1/6)s – (1/2)(s – 2) = (45/2)

Multiply 2 on both sides.

2 × (1/6)s – 2 × (1/2)(s – 2) = (45/2) × 2

(1/3)s – (s-2) = 45

Multiply 3 on both sides.

3 × (1/3)s – 3 ×(s-2) = 45 × 3

s – 3s + 6 = 135

-2s + 6 = 135

Subtract 6 on both sides

-2s + 6 – 6 = 135 – 6

-2s = 129

Divide (-2) on both sides.

-2s ÷ (-2) = 129 ÷ (-2)

s = -(129/2)

Question 39.
5(y + 1) = 3(3y + 4)
y = -(7/4)

Explanation:
Given, 5(y + 1) = 3(3y + 4)

5y + 5 = 9y + 12

Subtract 5 on both sides.

5y + 5 – 5 = 9y + 12 – 5

5y = 9y + 7

Subtract 5y on both sides.

5y – 5y = 9y + 7 – 5y

0 = 4y + 7

4y = -7

Divide 4 on both sides.

4y ÷ 4 = -7 ÷ 4

y = -(7/4)

Question 40.
2(b + 5) = 3(4 – b)
b =(2/5)

Explanation:
Given, 2(b + 5) = 3(4 – b)

2b + 10 = 12 – 3b

2b + 10 + 3b = 12 – 3b + 3b

5b + 10 = 12

Subtract 10 on both sides.

5b + 10 – 10 = 12 – 10

5b = 2

Divide 5 on both sides.

5b ÷ 5 = 2 ÷ 5

b =(2/5)

Question 41.

Math Journal Nelson solved the algebraic equation 3(2x + 5) = 17 as I shown below:
3(2x + 5) = 17
3(2x + 5) – 5 = 17 – 5
3(2x) = 12 6
x = 12
6x ÷ 6 = 12 ÷ 6
x = 2
Describe and correct the error Nelson made.
x = (1/3)

Explanation:
Given, 3(2x + 5) = 17

3 × 2x + 3 × 5 = 17

6x + 15 = 17

Subtract 15 on both sides

6x + 15 – 15 = 17 – 15

6x = 2

Divide 6 on both sides.

6x ÷ 6 = 2 ÷ 6

x = (2/6)

x = (1/3)

Question 42.
Math Journal Describe the steps you could use to solve 2(b – 5) + 3(b – 2) = 8 + 7(b – 4). Solve and show your work.
b = 2

Explanation:
Given, 2(b – 5) + 3(b – 2) = 8 + 7(b – 4)

2b – 10 +3b – 6 = 8 + 7b – 28

5b – 16 = 7b – 20

5b – 10 + 16 = 7b – 20 + 16

5b = 7b – 4

7b – 5b = 4

2b = 4

Divide 2 on both sides.

2b ÷ 2 = 4 ÷ 2

b = 2