Which of the following represents the value of p that satisfies the given equation? -2(4p … — Armed Services Vocational Aptitude Battery (ASVAB)

Which of the following represents the value of $p$ that satisfies the given equation?

-2(4p - 5) + \frac{1}{3}(15p - 12) = 2p - (7p - 14)

The correct answer is 4. To solve the equation, first distribute the outer terms across the parentheses on both sides:

-2(4p - 5)

becomes

-8p + 10

\frac{1}{3}(15p - 12)

becomes

5p - 4

, and

-(7p - 14)

becomes

-7p + 14

. Combining like terms on the left side (

-8p + 5p

and

10 - 4

) gives

-3p + 6

. On the right side, combining

2p

and

-7p

gives

-5p + 14

. Setting these equal gives

-3p + 6 = -5p + 14

. Adding

5p

to both sides yields

2p + 6 = 14

, and subtracting 6 from both sides gives

2p = 8

. Dividing by 2 results in

p = 4

Distribute the coefficients to remove parentheses on the left side.

-8p + 10 + 5p - 4 = 2p - (7p - 14)

Applying the distributive property is necessary to eliminate grouping symbols.

Distribute the negative sign to remove parentheses on the right side.

-8p + 10 + 5p - 4 = 2p - 7p + 14

Distributing the subtraction over the group allows all terms to be evaluated.

Combine like terms on each side of the equation independently.

-3p + 6 = -5p + 14

Simplifying both sides makes it easier to balance the equation and isolate the variable.

Add

5p

to both sides and subtract 6 from both sides.

2p = 8

Performing these inverse operations groups all variable terms on one side and all constant terms on the other.

Divide both sides by 2.

p = 4

Dividing by the coefficient isolates the variable

p

, revealing its final value.

Solving complex multi-step linear equations using the distributive property and combining like terms.

Question