How do you solve the inequality $| 7 x | > - 4$ $abs(7x) > -4$ ?

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Answer 1 · 2015-09-10T03:03:29

$- \frac{4}{7} ≺ x ≺ \frac{4}{7}$ $-4/7 -< x -< 4/7$

$| 7 x | ≻ 4$ $|7x| >- 4$ is equivalent to the following two inequalities:
$7 x ≻ 4$ $7x >- 4$ and $- 7 x ≻ 4$ $-7x >- 4$ .

Dividing out 7 and -7 gives us:
$x ≻ \frac{4}{7}$ $x >- 4/7$ and $- \frac{4}{7} ≻ x$ $-4/7 >- x$ .

Combining the two inequalities together gives:
$- \frac{4}{7} ≺ x ≺ \frac{4}{7}$ $-4/7 -< x -< 4/7$

How do you solve the inequality abs(7x) > -4|7x|>−4abs(7x) > -4?