Transform the absolute value inequality $| 2 - 2 h | \geq 7$ into two separate inequalities.
A) $2 - 2 h \leq 7$ or $2 - 2 h \geq - 7$
B) $2 - 2 h \geq 7$ or $2 - 2 h \geq 7$
C) $2 - 2 h \geq 7$ or $2 - 2 h \geq - 7$
D) $2 - 2 h \geq - 7$ or $2 - 2 h \leq - 7$
E) $2 - 2 h \geq 7$ or $2 - 2 h \leq - 7$

Question

Quizplus · Accepted Answer

To separate the absolute value inequality, we need to consider two cases, one where the expression inside the absolute value is positive and the other where it is negative. 
When $2 - 2h$ is positive, we have:
$$2-2h\geq7$$
Solving this inequality, we get:
$$h\leq- \frac{5}{2}$$
When $2 - 2h$ is negative, we have:
$$-(2-2h)\geq7$$
Simplifying, we get:
$$2h-2\leq-7$$
Solving this inequality, we get:
$$h\leq-\frac{5}{2}$$
Thus, combining the two inequalities, we get:
$$h\leq-\frac{5}{2}$$ or $$2-2h\geq7$$ or $$2-2h\leq-7$$
The final inequality can be further simplified as:
$$h\geq\frac{9}{4}$$ or $$h\leq-\frac{5}{2}$$

Transform the Absolute Value Inequality ∣2−2h∣≥7| 2 - 2 h | \geq 7∣2−2h∣≥7

Transform the Absolute Value Inequality $| 2 - 2 h | \geq 7$