How do you solve the inequality: $- \frac{1}{6} \leq 4 x - 4 < \frac{1}{3}$ $-1/6<= 4x-4<1/3$ ?

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Answer 1 · 2015-08-31T00:29:29

$x \in [\frac{23}{24}, \frac{26}{24})$ $x in [23/24, 26/24)$

You need to isolate $x$ $x$ between the two inequality signs. Start by adding $4$ $4$ to all sides

$-1/6 + 4 <= 4x - color(red)(cancel(color(black)(4))) + color(red)(cancel(color(black)(4))) < 1/3 + 4$

$23/6 <= 4x < 13/3$

Now divide all sides by $4$

$23/6 * 1/4 <= (color(red)(cancel(color(black)(4)))x)/color(red)(cancel(color(black)(4))) < 13/3 * 1/4$

This will get you

$23/24 <= x < 13/12$

which is equivalent to

$23/24 <= x < 26/24$

In interval notation, the solution set for this compound inequality is $x in [23/24, 26/24)$ .

How do you solve the inequality: -1/6<= 4x-4<1/3−16≤4x−4<13-1/6<= 4x-4<1/3?