What is |x|+|2x-8|<= |x+8| ?

The solution to |x|+|2x-8|<= |x+8| is 0<= x<= 8

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|x|+|2x-8|<= |x+8|

∣ x ∣ + ∣ 2 x - 8 ∣ \leq ∣ x + 8 ∣

0 \leq x \leq 8

Interval Notation

[0, 8]

Solution steps

∣ x ∣ + ∣ 2 x - 8 ∣ \leq ∣ x + 8 ∣

Find positive and negative intervals

x < - 8, - 8 \leq x < 0, 0 \leq x < 4, x \geq 4

Solve the inequality for each interval

No Solution or 0 \leq x < 4 or 4 \leq x \leq 8

Merge Overlapping Intervals

0 \leq x \leq 8

\frac{( 3 x + 1 )}{( x - 3 )} > 6

∣ z ∣ \leq 7

∣ 2 x + 5 ∣ > 0.5

- 4 x + 14 + 10 ∣ x - 2 ∣ < 12

∣ x + 2 ∣ \leq x + 3