Question

Solve the following absolute value equation for the unknown. Show all of your work for full credit. |-3h – 6| ≤ 3

Answer 1

Answer:

$-3 \le h \le 1$.

Step-by-step explanation:

Apply the property of absolute values: if $a \ge 0$, then $|x| \le a \iff -a \le x \le a$. By this property, $|- 3\, h - 6 | \le 3$ is equivalent to $-3 \le -3\, h - 6\le 3$. That's the same as saying that $-3\, h - 6 \ge -3$ and $-3\, h - 6 \le 3$.

Add $6$ to both sides of both inequalities:

$-3\, h \ge 3$ and $-3\, h \le 9$.

Divide both sides of both inequalities by $(-3)$. Note that because $-3 < 0$, dividing both sides of an equality by this number will flip the direction of the inequality sign.

• $-3\, h \ge 3$ would become $h \le -1$.
• $-3\, h \le 9$ would become $h \ge -3$.

Both inequalities are supposed to be true. Combining the two inequalities to obtain:

$-3 \le h \le 1$.