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# Find all solutions x of the inequality

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Find all solutions x of the inequality  $$\frac{5}{24} + \left|x-\frac{11}{48}\right| < \frac{5}{16}$$

Guest Jun 13, 2018
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$$\frac{5}{24}+|x-\frac{11}{48}|<\frac{5}{16}$$

1) Isolate the absolute value part
$$|x-\frac{11}{48}|<\frac{5}{48}$$

2) For absolute value inequalities, split the inequality into two parts, then solve.

For one of the parts, just drop the absolute value and solve.
For the second part, drop the absolute value, flip the inequality sign and make the other side negative.
$$x-\frac{11}{48}<\frac{5}{48}\\ x<\frac{16}{48}\\ x<\frac{1}{3}$$ and  $$x-\frac{11}{48}>-\frac{5}{48}\\ x>\frac{6}{48}\\ x>\frac{1}{8}$$
3) Turn that into interval notation.

(1/8)

$$(\frac{1}{8},\frac{1}{3})$$

ChowMein  Jun 13, 2018
edited by ChowMein  Jun 13, 2018
edited by ChowMein  Jun 13, 2018