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What should be the first step to solve the equation?
[tex]\[ 2x + 9(x-1) = 8(2x+2) - 5 \][/tex]

A. Combine like terms on each side of the equation.
B. Use the distributive property on each side of the equation.
C. Use the subtraction property of equality to subtract 5 from each side of the equation.
D. Use the addition property of equality to add [tex]\( 2x \)[/tex] to each side of the equation.



Answer :

GinnyAnswer
To solve the equation
[tex]\[ 2x + 9(x - 1) = 8(2x + 2) - 5 \][/tex]

The first step is to use the distributive property on each side of the equation. Here’s how we do that:

Step-by-Step Solution:

1. Apply the Distributive Property:

- On the left-hand side:
[tex]\[ 2x + 9(x - 1) \][/tex]
Applying the distributive property:
[tex]\[ 2x + 9(x - 1) = 2x + 9x - 9 = 11x - 9 \][/tex]

- On the right-hand side:
[tex]\[ 8(2x + 2) - 5 \][/tex]
Apply the distributive property:
[tex]\[ 8(2x + 2) = 8 \cdot 2x + 8 \cdot 2 = 16x + 16 \][/tex]
Then include the -5:
[tex]\[ 16x + 16 - 5 = 16x + 11 \][/tex]

So, after applying the distributive property, the equation
[tex]\[ 2x + 9(x - 1) = 8(2x + 2) - 5 \][/tex]
transforms to:
[tex]\[ 11x - 9 = 16x + 11 \][/tex]

This completes the first step.

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