Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations

Practice the problems of Math in Focus Grade 7 Workbook Answer Key Chapter 4 Lesson 4.1 Understanding Equivalent Equations to score better marks in the exam.

Math in Focus Grade 7 Course 2 A Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations

Math in Focus Grade 7 Chapter 4 Lesson 4.1 Guided Practice Answer Key

Copy and complete to state whether each pair of equations are equivalent equations. Give a reason for your answer.

Question 1.
Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 2
x – 3 + 4x = 5 and 5x = 2
x – 3 + 4x = 5
5x – 3 = 5 Group like terms.
5x – 3 + Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 = 5 + Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 Add Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 to both sides.
5x = Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 Simplify.
x – 3 + 4x = 5 Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 be rewritten as 5x = 2.
So, the equations have Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 solutions and are Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1
Answer:
No, they are not equivalent equations.

Explanation:
Given 1st equation, x – 3 + 4x = 5

It can also be written as 5x – 3 =5

Add 3 to both sides, 5x – 3 + 3 = 5 + 3

5x = 8

So, equation x – 3 + 4x = 5  cannot be written as 5x = 2

Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 3

Question 2.
x + 7 = 12 and 2x = 10
First solve x + 7 = 12.
x + 7 = 12
x + 7 – Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 = 12 – Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 Subtract Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 from both sides.
x = Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 Simplify.
Then check to see if Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 is the solution of the equation 2x = 10.
If x = Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1, 2x = 2 • Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 Substitute Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 for x.
= Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 a solution.
Because the equations have the Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 solution, they are Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 equations.
Answer:
Yes, Both are equivalent equations.

Explanation:
First, let’s solve x + 7 = 12

Subtract 7 on both sides.

x + 7 – 7 = 12 -7

x = 5

Lets consider second equation 2x = 10

substitute x= 5 which we got by solving  the 1st equation in the 2nd equation.

2.(5) = 10

Hence proved.

Question 3.
1.2x = 2.4 and x – 6 = 8
First solve x – 6 = 8.
x – 6 = 8
x – 6 + Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 = 8 + Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 Add Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 to both sides,
x = Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 Simplify.
Then check to see if Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 is the solution of the equation 1.2x = 2.4.
If x = Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1, 1.2x = 1.2 • Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 Substitute Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 for x.
= Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 a solution.
Because the equations have Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 solutions, they are Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 equations.
Answer:
No, they are not equivalent equations.

Explanation:
First, lets consider x – 6 = 8

Add 6 on both sides

x – 6 + 6 = 8 + 6

x = 14

Lets substitute x = 14  in the first equation.

1.2 x = 2.4

1.2(14) = 16.8

Both the equations are not equivalent equations.

Question 4.
\(\frac{2}{5}\)x = 4 and x = 10.
If x = 10, \(\frac{2}{5}\)x = \(\frac{2}{5}\) • 10 Substitute 10 for x.
= Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 a solution.
Because the equations have the Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 solution, they are Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 1 equations.
Answer:
Yes, both the equations have the same solution, they are equivalent equations.

Explanation:
Let’s consider first equation, (2/5)x =4

Let us  substitute the second equation, x =10 in first equation.

(2/5) × 10 = 4

Hence proved.

Both the equations have the same solution, they are equivalent equations.

Math in Focus Course 2A Practice 4.1 Answer Key

Tell whether each pair of equations are equivalent. Give a reason for your answer.

Question 1.
2x = 4 and 4x + 5 = 13
Answer:
Yes, Both the equations are equivalent.

Explanation:
Let us consider second equation, 4x + 5 = 13

Subtract 5 on both sides.

4x + 5 – 5 = 13 – 5

4x = 8

x = 8 ÷ 4

x = 2

Substitute x=2 in the first equation, 2x = 4

2(2) = 4

Hence proved.

Both the equations are equivalent.

Question 2.
-2x + 9 = 7 and —2x = 2
Answer:
No, both the equations are not equivalent.

Explanation:
Lets solve the first equation, -2x + 9 = 7

Subtract 9  on both sides.

-2x + 9 – 9 = 7 – 9

-2x = -2

The second equation is -2x = 2

So, both the equations are not equivalent.

Question 3.
5x – 4 + 3x = 8 and 8x = 12
Answer:
Both are equivalent equations.

Explanation:
Lets us consider first equation, 5x – 4 + 3x = 8

8x – 4 = 8

8x = 8 + 4

8x = 12

As we derived second equation from the first equation, both are equivalent equations.

Question 4.
\(\frac{3}{4}\)x – 7 = 2 and x = 12
Answer:
Yes, both are equivalent equations.

Explanation:
Let us consider first equation, (3/4)x = 2

Substitute, the second equation, x = 12 in the first equation.

(3/4)(12) – 7 = (3).(3) – 7

=9 – 7

=2

Hence proved. Both are equivalent equations.

Match each equation with an equivalent equation.

Math in Focus Grade 7 Chapter 4 Lesson 4.1 Answer Key Understanding Equivalent Equations 4
Answer:
5 – d
6 – c
7 – e
8 – a
9 – g
10 – f
11 – b

Explanation:
5.  0.5x + 1 = 1.5

0.5x = 1.5 – 1 = 0.5

x = 0.5 ÷ 0.5

x = 1

We can match 5th equation with equation (d) on the other side.

6. 9 + 3.5x = 16

Let us solve the equation

3.5x = 16 – 9

3.5x = 7

x = 7 ÷ 3.5

x = 2

We can match the equation (3/2)x = 3

x = 3 × (2/3)

x = 2

Hence both are same.

7. (4/5)x =4

4x = 20

x =5

We can match 7th equation with equation (e) on the other side.

2x =10

x =5

Hence Matched.

8.  2x + (1/2) = (7/2)

2x = (7/2) – (1/2)

2x = (6/2)

2x = 3

x = 3/2

As option (a) is 6x =9

It can be also written as 3/2 as both are dividends of 3.

9. x – 8.3 = 1.3

x = 1.3 + 8.3

x = 9.6

Option (g) is  (1/2)x = 4.8

x =9.6

Hence matched.

10. 13.9 = 2.5x

x = 13.9 ÷ 2.5

x = 5.56

Option (f) is 1.2 + x = 6.76

x = 6.76 – 1.2

x =5.56

Hence proved.

11. 4x = (4/9)

x = 1/9

We can match with option (b).

(3/5)x = (1/15)

x = (1/9)

Solve.

Question 12.
Math Journal Max was asked to write to \(\frac{2}{3}\)x = 3 – x. He wrote the following:
\(\frac{2}{3}\)x = 3 – x
\(\frac{2}{3}\)x ∙ 3 = 3 ∙ 3 – x
2x = 9 – x
He concluded that \(\frac{2}{3}\)x = 3 – x and 2x = 9 \(\frac{2}{3}\) x are equivalent equations. Do you agree with his conclusion? Give a reason for your answer.
Answer:
No, I don’t agree with Max, both are not equivalent equations.

Explanation:
Let us consider first equation, (2/3)x = 3 – x

2x = 9 -3x (Max gave the equation 2x = 9 – x which is wrong, if we multiplied 3 on both sides not only it is multiplied with 3 it is also multiplies with x. so it is 2x = 9 -3x)

5x = 9

x = 9/5

x = 1.8

The second equation, 9(2/3)x =2x

substitute x =1.8 in the second equation

2 (1.8) = 9(2/3)(1.8)

3.6 = 10.8

Hence the both the equations are not equivalent.

 

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