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Popular >

2<= |3x-1|-6

Solution

2 \leq ∣ 3 x - 1 ∣ - 6

Solution

x \leq - \frac{7}{3} or x \geq 3

+2

Interval Notation

(- \infty, - \frac{7}{3}] \cup [3, \infty)

Decimal Notation

x \leq - 2.33333 \dots or x \geq 3

Solution steps

2 \leq ∣ 3 x - 1 ∣ - 6

Switch sides

∣ 3 x - 1 ∣ - 6 \geq 2

Move

6

to the right side

∣ 3 x - 1 ∣ \geq 8

Apply absolute rule: If

∣ u ∣ \geq a, a > 0

then

u \leq - a

or

u \geq a

3 x - 1 \leq - 8 or 3 x - 1 \geq 8

3 x - 1 \leq - 8 or 3 x - 1 \geq 8

x \leq - \frac{7}{3} or x \geq 3

Popular Examples

(a+2)/3+(a-2)/5 = 12/15

\frac{a + 2}{3} + \frac{a - 2}{5} = \frac{12}{15}

6(x-5)-5(3-2x)=3(9-11x)

6 (x - 5) - 5 (3 - 2 x) = 3 (9 - 11 x)

factor 81x^2-169y^2 factor

81 x^{2} - 169 y^{2}

simplify (sqrt(2))/2+sqrt(2)simplify

\frac{2}{2} + 2

factor a^2+a-380 factor

a^{2} + a - 380

Frequently Asked Questions (FAQ)

What is 2<= |3x-1|-6 ?
The solution to 2<= |3x-1|-6 is x<=-7/3 \lor x>= 3