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Popular >

-4|3x-1|<=-16

Solution

- 4 ∣ 3 x - 1 ∣ \leq - 16

Solution

x \leq - 1 or x \geq \frac{5}{3}

+2

Interval Notation

(- \infty, - 1] \cup [\frac{5}{3}, \infty)

Decimal Notation

x \leq - 1 or x \geq 1.66666 \dots

Solution steps

- 4 ∣ 3 x - 1 ∣ \leq - 16

Multiply both sides by

- 1

4 ∣ 3 x - 1 ∣ \geq 16

Divide both sides by

4

∣ 3 x - 1 ∣ \geq 4

Apply absolute rule: If

∣ u ∣ \geq a, a > 0

then

u \leq - a

or

u \geq a

3 x - 1 \leq - 4 or 3 x - 1 \geq 4

3 x - 1 \leq - 4 or 3 x - 1 \geq 4

x \leq - 1 or x \geq \frac{5}{3}

Popular Examples

x^{3} - x < 0

3 + ∣ x - 3 ∣ > \frac{4}{7}

x^{2} + 4 x - 8 = 0

factor 4x^4-17x^2+4 factor

4 x^{4} - 17 x^{2} + 4

\frac{2 x}{3} - 2 = - 8

Frequently Asked Questions (FAQ)

What is -4|3x-1|<=-16 ?
The solution to -4|3x-1|<=-16 is x<=-1\lor x>= 5/3