What is |(7-8x)/4 |<= 2 ?

The solution to |(7-8x)/4 |<= 2 is -1/8 <= x<= 15/8

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|(7-8x)/4 |<= 2

\frac{7 - 8 x}{4} \leq 2

- \frac{1}{8} \leq x \leq \frac{15}{8}

Interval Notation

[- \frac{1}{8}, \frac{15}{8}]

Decimal Notation

- 0.125 \leq x \leq 1.875

Solution steps

\frac{7 - 8 x}{4} \leq 2

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 2 \leq \frac{7 - 8 x}{4} \leq 2

\frac{7 - 8 x}{4} \geq - 2 and \frac{7 - 8 x}{4} \leq 2

x \leq \frac{15}{8} and x \geq - \frac{1}{8}

Merge Overlapping Intervals

- \frac{1}{8} \leq x \leq \frac{15}{8}

a + 11 = 20

9 (2 x + 15) = 45

\frac{( 5 - 3 x ) ^{2}}{( 2 x - 5 ) ^{3}} > 0

6 e^{\frac{π}{6} i}

5 x + 3 = x + 3