What is |(4x-5)/2 |<= 1/3 ?

The solution to |(4x-5)/2 |<= 1/3 is 13/12 <= x<= 17/12

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|(4x-5)/2 |<= 1/3

\frac{4 x - 5}{2} \leq \frac{1}{3}

\frac{13}{12} \leq x \leq \frac{17}{12}

Interval Notation

[\frac{13}{12}, \frac{17}{12}]

Decimal Notation

1.08333 \dots \leq x \leq 1.41666 \dots

Solution steps

\frac{4 x - 5}{2} \leq \frac{1}{3}

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- \frac{1}{3} \leq \frac{4 x - 5}{2} \leq \frac{1}{3}

\frac{4 x - 5}{2} \geq - \frac{1}{3} and \frac{4 x - 5}{2} \leq \frac{1}{3}

x \geq \frac{13}{12} and x \leq \frac{17}{12}

Merge Overlapping Intervals

\frac{13}{12} \leq x \leq \frac{17}{12}

7 x + 32 < 18

(\frac{6 ^{\frac{1}{5}}}{6 ^{\frac{2}{5}}})^{3}

\frac{4 ( 9 )}{9 ( 9 ) ^{\frac{1}{2}}}

\frac{( 3 x + 1 )}{2} - \frac{1}{3} < 1

30 - 11 x + x^{2}

What is |(4x-5)/2 |<= 1/3 ?
The solution to |(4x-5)/2 |<= 1/3 is 13/12 <= x<= 17/12