What is (|2x+6|)/3 <2 ?

The solution to (|2x+6|)/3 <2 is -6<x<0

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(|2x+6|)/3 <2

\frac{∣ 2 x + 6 ∣}{3} < 2

- 6 < x < 0

Interval Notation

(- 6, 0)

Solution steps

\frac{∣ 2 x + 6 ∣}{3} < 2

Multiply both sides by

3

∣ 2 x + 6 ∣ < 6

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 6 < 2 x + 6 < 6

2 x + 6 > - 6 and 2 x + 6 < 6

x > - 6 and x < 0

Merge Overlapping Intervals

- 6 < x < 0

7 x^{2} + 1 = 8

\frac{7}{16} = \frac{x}{4}

\frac{x - 7}{5} = \frac{x - 8}{4}

∣ 4 x + 8 ∣ + ∣ 5 x ∣ \leq 2

2 ∣ x + 4 ∣ + 1 < 15