What is |11x-2|<= 16 ?

The solution to |11x-2|<= 16 is -14/11 <= x<= 18/11

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|11x-2|<= 16

∣ 11 x - 2 ∣ \leq 16

- \frac{14}{11} \leq x \leq \frac{18}{11}

Interval Notation

[- \frac{14}{11}, \frac{18}{11}]

Decimal Notation

- 1.27272 \dots \leq x \leq 1.63636 \dots

Solution steps

∣ 11 x - 2 ∣ \leq 16

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 16 \leq 11 x - 2 \leq 16

11 x - 2 \geq - 16 and 11 x - 2 \leq 16

x \geq - \frac{14}{11} and x \leq \frac{18}{11}

Merge Overlapping Intervals

- \frac{14}{11} \leq x \leq \frac{18}{11}

17 - 3 x \geq 56

\frac{2}{3} 16 n

20 x - 15

3 a^{2} b^{2} + 15 a b^{3}

10 x^{2} - 120 x - 10