What is |x-4|+|x+3|-3>= |x| ?

The solution to |x-4|+|x+3|-3>= |x| is True for all x

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|x-4|+|x+3|-3>= |x|

∣ x - 4 ∣ + ∣ x + 3 ∣ - 3 \geq ∣ x ∣

True for all x

Interval Notation

(- \infty, \infty)

Solution steps

∣ x - 4 ∣ + ∣ x + 3 ∣ - 3 \geq ∣ x ∣

Find positive and negative intervals

x < - 3, - 3 \leq x < 0, 0 \leq x < 4, x \geq 4

Solve the inequality for each interval

x < - 3 or - 3 \leq x < 0 or 0 \leq x < 4 or x \geq 4

Merge Overlapping Intervals

True for all x

(- 3)^{- 2}

6 x^{2} - 5 x = 56

∣ w - 5 ∣ \leq 1

12 x + 18

(40 x^{3} - 15 x^{2}) (- 16 x + 6)

What is |x-4|+|x+3|-3>= |x| ?
The solution to |x-4|+|x+3|-3>= |x| is True for all x