Question

solve the following absolute value equation.

\\|5p + 42| = |6p - 9|\\

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the solution set is \\{\quad\\}.
(simplify your answer. use a comma to separate answers as needed.)
b. the solution set is \\{\\} or \varnothing.

Explanation:

⚡ Using what you learned: Solving Absolute Value Equations

Step 1: Split into two cases

An equation of the form \( |a| = |b| \) is true if \( a = b \) or \( a = -b \).

$$ 5p + 42 = 6p - 9 \quad \text{or} \quad 5p + 42 = -(6p - 9) $$

Step 2: Solve Case 1

$$ 5p + 42 = 6p - 9 $$

$$ 42 + 9 = 6p - 5p $$

$$ p = 51 $$

Step 3: Solve Case 2

$$ 5p + 42 = -6p + 9 $$

$$ 5p + 6p = 9 - 42 $$

$$ 11p = -33 $$

$$ p = -3 $$

Answer:

A. The solution set is \( \{51, -3\} \).