How do you solve $|6h|<12$ ?

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Answer 1 · 2017-01-09T20:04:14

See full explanation below.

Because this problem contains an absolute value function we must solve this problem for both -12 and +12.

Also, because it is an inequality we must solve a system on inequalities and not just a single equation.

We can rewrite this problem as:

$-12 < 6h < 12$

Now we can divide each portion of the system by $color(red)(6)$ to solve for $h$ while keeping the system balanced:

$-12/color(red)(6) < (6h)/color(red)(6) < 12/color(red)(6)$

$-2 < (color(red)(cancel(color(black)(6)))h)/cancel(color(red)(6)) < 2$

$-2 < h < 2$

How do you solve |6h|<12|6h|<12?