Question

for the absolute value equation |2x + 5| = 14, which of the following are solutions? there may be more than one correct choice. please select all that apply. options: 7/5, 9/2, -19/2, -6/7, 8/7

Explanation:

Step1: Split absolute value equation

An absolute value equation $|A| = B$ splits into $A=B$ and $A=-B$. So:
$2x + 5 = 14$ and $2x + 5 = -14$

Step2: Solve first equation

Isolate $x$ by subtracting 5, then divide by 2:
$2x = 14 - 5 = 9$
$x = \frac{9}{2}$

Step3: Solve second equation

Isolate $x$ by subtracting 5, then divide by 2:
$2x = -14 - 5 = -19$
$x = -\frac{19}{2}$

Step4: Match to options

Compare solutions to given choices.

Answer:

$\square \frac{7}{5}$
$\boxtimes \frac{9}{2}$
$\boxtimes -\frac{19}{2}$
$\square -\frac{6}{7}$
$\square \frac{8}{7}$
The correct solutions are $\frac{9}{2}$ and $-\frac{19}{2}$.