Evaluate the given algebraic equation to solve for p: 7 - 3(p + 2) = p - 7 Which of the fo… — Armed Services Vocational Aptitude Battery (ASVAB)

Evaluate the given algebraic equation to solve for $p$ :

7 - 3(p + 2) = p - 7

Which of the following represents the correct solution for $p$ ?

The correct value is 2.

The correct approach involves distributing the

-3

into the parentheses to get

7 - 3p - 6

, combining like terms to get

1 - 3p

, and then balancing the equation to solve for

p

. Adding

3p

to both sides yields

1 = 4p - 7

, and adding

7

gives

8 = 4p

, which simplifies to

p = 2

Apply the distributive property to the left side of the equation.

7 - 3p - 6 = p - 7

The -3 must be multiplied by both

p

and

2

to eliminate the parentheses.

Combine the constant terms on the left side.

1 - 3p = p - 7

Combining

7

and

-6

simplifies the equation before moving terms across the equals sign.

Add

3p

to both sides of the equation.

1 = 4p - 7

This groups all terms containing the variable

p

on the right side.

Add

7

to both sides and divide by

4

8 = 4p \Rightarrow p = 2

This isolates the variable

p

to find the final numerical solution.

Solving Linear Equations with Distribution

Question