Question

21 multiple choice 2 points
what is the solution to priyas problem?
$2|x + 4| - 3 < 3$
$2|x + 4| < 6$
$|x + 4| < 3$
$circ$ $x < -7$ and $x > -1$
$circ$ $x < -1$ and $x < -7$
$circ$ $-7 < x < -1$
$circ$ $x = -7, -1$

Explanation:

Step1: Isolate absolute value term

Start with the given inequality:
$$2|x+4| - 3 < 3$$
Add 3 to both sides:
$$2|x+4| < 6$$

Step2: Simplify the inequality

Divide both sides by 2:
$$|x+4| < 3$$

Step3: Solve absolute value inequality

Recall $|A| < B$ translates to $-B < A < B$. Substitute $A=x+4$, $B=3$:
$$-3 < x+4 < 3$$

Step4: Solve for x

Subtract 4 from all parts:
$$-3 - 4 < x < 3 - 4$$
$$-7 < x < -1$$

Answer:

$-7 < x < -1$