question solution

1
Solve the inequality

4 - 5∣ 2 - 3 x ∣ \leq - 6

Rearrange the terms

Rearrange variables to the left side of the equation

- 5∣ 2 - 3 x ∣ \leq - 6 - 4

- 5∣ 2 - 3 x ∣ \leq - 6 - 4

Calculate

Calculate the sum or difference

- 5∣ 2 - 3 x ∣ \leq - 10

- 5∣ 2 - 3 x ∣ \leq - 10

Divide both sides

Divide both sides of the inequality by the coefficient of variable

∣ 2 - 3 x ∣ \geq \frac{- 10}{- 5}

∣ 2 - 3 x ∣ \geq \frac{- 10}{- 5}

Reduce

Reduce the fraction

∣ 2 - 3 x ∣ \geq 2

∣ 2 - 3 x ∣ \geq 2

Transform the inequality

Convert theabsolute inequalityto standard inequality

2 - 3 x \geq 2

2 - 3 x \leq - 2

2 - 3 x \geq 2

2 - 3 x \leq - 2

More steps

Show more steps

2 - 3 x \geq 2

Rearrange variables to the left side of the equation

- 3 x \geq 2 - 2

Calculate the sum or difference

- 3 x \geq 0

Divide both sides of the inequality by the coefficient of variable

x \leq 0

Divide both sides of the inequality by the coefficient of variable

x \leq 0

2 - 3 x \leq - 2

Rearrange variables to the left side of the equation

- 3 x \leq - 2 - 2

Calculate the sum or difference

- 3 x \leq - 4

Divide both sides of the inequality by the coefficient of variable

x \geq \frac{- 4}{- 3}

Determine the sign for multiplication or division

x \geq \frac{4}{3}

Determine the sign for multiplication or division

x \geq \frac{4}{3}

x \leq 0

x \geq \frac{4}{3}

Express solution set in interval notation:

(- \infty, 0] \cup [\frac{4}{3}, \infty)

(- \infty, 0] \cup [\frac{4}{3}, \infty)

Answer

(- \infty, 0] \cup [\frac{4}{3}, \infty)