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Popular >

5-2*|1+3x|<=-3

Solution

5 - 2 \cdot ∣ 1 + 3 x ∣ \leq - 3

Solution

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

+2

Interval Notation

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

Decimal Notation

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

Solution steps

5 - 2 ∣ 1 + 3 x ∣ \leq - 3

Move

5

to the right side

- 2 ∣ 1 + 3 x ∣ \leq - 8

Multiply both sides by

- 1

2 ∣ 1 + 3 x ∣ \geq 8

Divide both sides by

2

∣ 1 + 3 x ∣ \geq 4

Apply absolute rule: If

∣ u ∣ \geq a, a > 0

then

u \leq - a

or

u \geq a

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

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

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

Popular Examples

∣ 3 x - 4 ∣ + 2 = 1

- 5.3 = \frac{x}{5} + 7.2

(x+5)(x^2-4)(x-6)<0

(x + 5) (x^{2} - 4) (x - 6) < 0

simplify \sqrt[3]{256x^{10}y^7}simplify

3 + v \leq - 9

Frequently Asked Questions (FAQ)

What is 5-2*|1+3x|<=-3 ?
The solution to 5-2*|1+3x|<=-3 is x<=-5/3 \lor x>= 1