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].
