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Select the correct answer.

What is the solution to [tex]|2x + 3| = 15[/tex]?

A. [tex]x = 6[/tex]

B. [tex]x = 6[/tex] or [tex]x = -6[/tex]

C. [tex]x = 6[/tex] or [tex]x = -9[/tex]

D. No solutions exist.

Sagot :

GinnyAnswer
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]
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