To solve the equation \( |2x + 3| = 15 \), we need to consider the definition of absolute value. The absolute value of a number equals that number or the opposite of that number. This gives us two separate equations to solve:
1. \( 2x + 3 = 15 \)
2. \( 2x + 3 = -15 \)
Let's solve each case step-by-step:
### Case 1: \( 2x + 3 = 15 \)
1. Subtract 3 from both sides of the equation:
[tex]\[ 2x + 3 - 3 = 15 - 3 \][/tex]
[tex]\[ 2x = 12 \][/tex]
2. Divide both sides by 2 to solve for \( x \):
[tex]\[ \frac{2x}{2} = \frac{12}{2} \][/tex]
[tex]\[ x = 6 \][/tex]
### Case 2: \( 2x + 3 = -15 \)
1. Subtract 3 from both sides of the equation:
[tex]\[ 2x + 3 - 3 = -15 - 3 \][/tex]
[tex]\[ 2x = -18 \][/tex]
2. Divide both sides by 2 to solve for \( x \):
[tex]\[ \frac{2x}{2} = \frac{-18}{2} \][/tex]
[tex]\[ x = -9 \][/tex]
Thus, the solutions to the equation \( |2x + 3| = 15 \) are \( x = 6 \) and \( x = -9 \).
Therefore, the correct answer is:
C. [tex]\( x = 6 \)[/tex] or [tex]\( x = -9 \)[/tex]
