Question

9 multiple answer 2 points
solve $|x - 3| + 9 = 14$
8
-2
-8
2
10 multiple answer 2 points
solve $-2|x + 1| = -16$
-9
-7
7
9

Explanation:

Problem 9

Step1: Isolate absolute value term

Subtract 9 from both sides.
$|x-3| = 14 - 9$
$|x-3| = 5$

Step2: Split into two equations

Absolute value equals positive/negative 5.
$x-3 = 5$ or $x-3 = -5$

Step3: Solve first equation

Add 3 to both sides.
$x = 5 + 3 = 8$

Step4: Solve second equation

Add 3 to both sides.
$x = -5 + 3 = -2$

Problem 10

Step1: Isolate absolute value term

Divide both sides by -2.
$|x+1| = \frac{-16}{-2}$
$|x+1| = 8$

Step2: Split into two equations

Absolute value equals positive/negative 8.
$x+1 = 8$ or $x+1 = -8$

Step3: Solve first equation

Subtract 1 from both sides.
$x = 8 - 1 = 7$

Step4: Solve second equation

Subtract 1 from both sides.
$x = -8 - 1 = -9$

Answer:

Problem 9:

8, -2

Problem 10:

-9, 7