What is 10-2|3x+2|>= 4 ?

The solution to 10-2|3x+2|>= 4 is -5/3 <= x<= 1/3

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10-2|3x+2|>= 4

10 - 2 ∣ 3 x + 2 ∣ \geq 4

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

Interval Notation

[- \frac{5}{3}, \frac{1}{3}]

Decimal Notation

- 1.66666 \dots \leq x \leq 0.33333 \dots

Solution steps

10 - 2 ∣ 3 x + 2 ∣ \geq 4

Move

10

to the right side

- 2 ∣ 3 x + 2 ∣ \geq - 6

Multiply both sides by

- 1

2 ∣ 3 x + 2 ∣ \leq 6

Divide both sides by

2

∣ 3 x + 2 ∣ \leq 3

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 3 \leq 3 x + 2 \leq 3

3 x + 2 \geq - 3 and 3 x + 2 \leq 3

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

Merge Overlapping Intervals

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

x^{2} - 5 x - 8 = 0

3 (- 5 x + 4) + 5 x - 1 = - 39

27 m^{2} - 48 = 0

∣ x - 1 ∣ = 2 x + 1

0.654 = 60.9 (x)