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

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

∣ x ∣ - x + 2 \leq 2 ∣ x - 4 ∣

x \leq 3 or x \geq 5

Interval Notation

(- \infty, 3] \cup [5, \infty)

Solution steps

∣ x ∣ - x + 2 \leq 2 ∣ x - 4 ∣

Find positive and negative intervals

x < 0, 0 \leq x < 4, x \geq 4

Solve the inequality for each interval

x < 0 or 0 \leq x \leq 3 or x \geq 5

Merge Overlapping Intervals

x \leq 3 or x \geq 5

2 x^{2} - 13 x = 1

- 16 = - 6 + \frac{x}{8}

\frac{- 5}{2 ^{2}}

∣ 2 w - 1 ∣ - 2 = 3

n^{2} + 8 n - 11 = - 5