Question

|x| = 7 solve the absolute value equation. {7} no solution {0, 7} {-7, 7}

Explanation:

Step1: Recall absolute value definition

The absolute value of a number \( x \), denoted \( |x| \), is the distance of \( x \) from 0 on the number line. So, if \( |x| = a \) (where \( a \geq 0 \)), then \( x = a \) or \( x = -a \).

Step2: Apply to the equation \( |x| = 7 \)

Using the definition, we have two cases:

• Case 1: \( x = 7 \) (since \( |7| = 7 \))
• Case 2: \( x = -7 \) (since \( |-7| = 7 \))

So the solutions are \( x = -7 \) and \( x = 7 \).

Answer:

\(\{-7, 7\}\)