Question

Kelsey solved the following equation:

Answer 1

Answer:

I took the test it is  1. Distributive property 2. Combine like terms 3. Addition property of equality 4. Division property of equality

Answer 2

The correct justifications Kelsey used to solve this equation is:

1. distributive property

2. combine like terms

3. addition property of equality

4. division property of equality

Solution:

Given that,

Kelsey solved the following equation:

$7x - \frac{1}{2}(8x+2) = 6$

Step 1:

By distributive property,

a(b + c) = ab + bc

Therefore,

$7x - (\frac{1}{2} \times 8x)+( \frac{-1}{2} \times 2)= 6\\\\7x - 4x - 1 = 6$

Step 2:

Combine the like terms

7x - 4x - 1 = 6

3x - 1 = 6

Step 3:

Addition property of equality

The property means that when we add the same number to both sides of an equation, the sides remain equal

3x - 1 = 6

Add 1 on both sides

3x - 1 + 1 = 6 + 1

3x = 7

Step 4:

Division property of equality

The Division Property of Equality means that when we divide both sides of an equation by the same non zero number, the sides remain equal

3x = 7

Divide both sides by 3

$\frac{3x}{3} = \frac{7}{3}\\\\x = \frac{7}{3}$

Thus the correct justifications Kelsey used to solve this equation is:

1. distributive property. 2. combine like terms. 3. addition property of equality. 4. division property of equality