What is |2x-1/3 |<= 8 ?

The solution to |2x-1/3 |<= 8 is -23/6 <= x<= 25/6

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|2x-1/3 |<= 8

2 x - \frac{1}{3} \leq 8

- \frac{23}{6} \leq x \leq \frac{25}{6}

Interval Notation

[- \frac{23}{6}, \frac{25}{6}]

Decimal Notation

- 3.83333 \dots \leq x \leq 4.16666 \dots

Solution steps

2 x - \frac{1}{3} \leq 8

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 8 \leq 2 x - \frac{1}{3} \leq 8

2 x - \frac{1}{3} \geq - 8 and 2 x - \frac{1}{3} \leq 8

x \geq - \frac{23}{6} and x \leq \frac{25}{6}

Merge Overlapping Intervals

- \frac{23}{6} \leq x \leq \frac{25}{6}

\frac{( \frac{4}{9} ) ^{- 2}}{( \frac{27}{8} ) ^{- 3}}

lo g_{\frac{1}{4}} (5)

\frac{75}{48}

ln (9)

12 = - 15 x - 6