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To solve the equation [tex]\( |2x + 3| = 17 \)[/tex], you need to consider the definition of absolute value. The absolute value equation [tex]\( |A| = B \)[/tex] implies two separate equations: [tex]\( A = B \)[/tex] and [tex]\( A = -B \)[/tex].
Here's the step-by-step process to solve [tex]\( |2x + 3| = 17 \)[/tex]:
1. Consider the first case:
[tex]\[ 2x + 3 = 17 \][/tex]
2. Solve for [tex]\( x \)[/tex] in this first case:
[tex]\[ 2x + 3 = 17 \][/tex]
Subtract 3 from both sides:
[tex]\[ 2x = 17 - 3 \][/tex]
Simplify:
[tex]\[ 2x = 14 \][/tex]
Divide both sides by 2:
[tex]\[ x = \frac{14}{2} \][/tex]
Simplify:
[tex]\[ x = 7 \][/tex]
3. Now consider the second case:
[tex]\[ 2x + 3 = -17 \][/tex]
4. Solve for [tex]\( x \)[/tex] in the second case:
[tex]\[ 2x + 3 = -17 \][/tex]
Subtract 3 from both sides:
[tex]\[ 2x = -17 - 3 \][/tex]
Simplify:
[tex]\[ 2x = -20 \][/tex]
Divide both sides by 2:
[tex]\[ x = \frac{-20}{2} \][/tex]
Simplify:
[tex]\[ x = -10 \][/tex]
Therefore, the solutions to the equation [tex]\( |2x + 3| = 17 \)[/tex] are [tex]\( x = 7 \)[/tex] and [tex]\( x = -10 \)[/tex].
So, the correct answer is:
A. [tex]\( x = 7 \)[/tex] and [tex]\( x = -10 \)[/tex].
Here's the step-by-step process to solve [tex]\( |2x + 3| = 17 \)[/tex]:
1. Consider the first case:
[tex]\[ 2x + 3 = 17 \][/tex]
2. Solve for [tex]\( x \)[/tex] in this first case:
[tex]\[ 2x + 3 = 17 \][/tex]
Subtract 3 from both sides:
[tex]\[ 2x = 17 - 3 \][/tex]
Simplify:
[tex]\[ 2x = 14 \][/tex]
Divide both sides by 2:
[tex]\[ x = \frac{14}{2} \][/tex]
Simplify:
[tex]\[ x = 7 \][/tex]
3. Now consider the second case:
[tex]\[ 2x + 3 = -17 \][/tex]
4. Solve for [tex]\( x \)[/tex] in the second case:
[tex]\[ 2x + 3 = -17 \][/tex]
Subtract 3 from both sides:
[tex]\[ 2x = -17 - 3 \][/tex]
Simplify:
[tex]\[ 2x = -20 \][/tex]
Divide both sides by 2:
[tex]\[ x = \frac{-20}{2} \][/tex]
Simplify:
[tex]\[ x = -10 \][/tex]
Therefore, the solutions to the equation [tex]\( |2x + 3| = 17 \)[/tex] are [tex]\( x = 7 \)[/tex] and [tex]\( x = -10 \)[/tex].
So, the correct answer is:
A. [tex]\( x = 7 \)[/tex] and [tex]\( x = -10 \)[/tex].
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