What is |x+4|<= |2x-6| ?

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|x+4|<= |2x-6|

∣ x + 4 ∣ \leq ∣ 2 x - 6 ∣

x \leq \frac{2}{3} or x \geq 10

Interval Notation

(- \infty, \frac{2}{3}] \cup [10, \infty)

Decimal Notation

x \leq 0.66666 \dots or x \geq 10

Solution steps

∣ x + 4 ∣ \leq ∣ 2 x - 6 ∣

Find positive and negative intervals

x < - 4, - 4 \leq x < 3, x \geq 3

Solve the inequality for each interval

x < - 4 or - 4 \leq x \leq \frac{2}{3} or x \geq 10

Merge Overlapping Intervals

x \leq \frac{2}{3} or x \geq 10

5 x - 10

\frac{4}{6} = \frac{m}{9}

\frac{7 + i}{- 6 - 2 i}

\frac{4}{5} x = 20

∣ - 9 x - 7 ∣ = 17