What is |x|+|x-4|>4 ?

The solution to |x|+|x-4|>4 is x 4

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|x|+|x-4|>4

∣ x ∣ + ∣ x - 4 ∣ > 4

x < 0 or x > 4

Interval Notation

(- \infty, 0) \cup (4, \infty)

Solution steps

∣ x ∣ + ∣ x - 4 ∣ > 4

Find positive and negative intervals

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

Solve the inequality for each interval

x < 0 or No Solution or x > 4

Merge Overlapping Intervals

x < 0 or x > 4

(b) ∣ x + 2 ∣ + 2 \geq 0

\frac{( 3 x + 6 )}{9} \geq 5

4 ∣ x - 9 ∣ > 16

x^{2} - ∣ 5 x + 6 ∣ > 0

x^{2} + 5 x < 6, ∣ x + 1 ∣ \leq 1