Solve the inequality. $| x + 4 | \leq 10$
A) $[ 4,10 ]$
B) $( - \infty , - 14 ] \cup [ 6 , \infty )$
C) $-$ 14, 6
D) $\phi$

Question

Quizplus · Accepted Answer

The inequality $| x + 4 | \leq 10$ means that the expression inside the absolute value, $x + 4$, is at most 10 units away from 0 on the number line. This leads to two cases: $x + 4 \leq 10$ and $x + 4 \geq -10$. Solving these gives $x \leq 6$ and $x \geq -14$, respectively, which means $x$ is in the interval $[-14, 6]$. However, the correct notation for the interval should be as an interval, not as a pair of numbers, indicating a mistake in the provided choices.

Solve the Inequality ∣x+4∣≤10| x + 4 | \leq 10∣x+4∣≤10 A) [4,10][ 4,10 ][4,10]

Solve the Inequality $| x + 4 | \leq 10$ A) $[ 4,10 ]$