What is |((2x-7))/4 |<= 1/3 ?

The solution to |((2x-7))/4 |<= 1/3 is 17/6 <= x<= 25/6

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|((2x-7))/4 |<= 1/3

\frac{( 2 x - 7 )}{4} \leq \frac{1}{3}

\frac{17}{6} \leq x \leq \frac{25}{6}

Interval Notation

[\frac{17}{6}, \frac{25}{6}]

Decimal Notation

2.83333 \dots \leq x \leq 4.16666 \dots

Solution steps

\frac{2 x - 7}{4} \leq \frac{1}{3}

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- \frac{1}{3} \leq \frac{2 x - 7}{4} \leq \frac{1}{3}

\frac{2 x - 7}{4} \geq - \frac{1}{3} and \frac{2 x - 7}{4} \leq \frac{1}{3}

x \geq \frac{17}{6} and x \leq \frac{25}{6}

Merge Overlapping Intervals

\frac{17}{6} \leq x \leq \frac{25}{6}

16 x y^{2} + 28 x y + 8 y

x^{2} + 12 x = - 32

25 p^{2} - 40 p + 16

- 6 < x - 4 \leq 1

x^{2} + 3 x + 2 + x^{2} - 1 = 0

What is |((2x-7))/4 |<= 1/3 ?
The solution to |((2x-7))/4 |<= 1/3 is 17/6 <= x<= 25/6