What is |x-3|-|x-3|-|x+4|<= 10 ?

The solution to |x-3|-|x-3|-|x+4|<= 10 is True for all x

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|x-3|-|x-3|-|x+4|<= 10

∣ x - 3 ∣ - ∣ x - 3 ∣ - ∣ x + 4 ∣ \leq 10

True for all x

Solution steps

∣ x - 3 ∣ - ∣ x - 3 ∣ - ∣ x + 4 ∣ \leq 10

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 < 3 or x \geq 3

Merge Overlapping Intervals

True for all x

\frac{( x - 3 )}{( x + 1 )} \leq 1

x - 1 - x^{2} \leq x^{2} - 3 x + 4

x^{2} - 5 ∣ x ∣ + 6 < 0

\frac{( 3 x )}{( x ^{2} - 4 )} \leq 1

∣ 5 x ∣ < ∣ 10 - 5 x ∣

What is |x-3|-|x-3|-|x+4|<= 10 ?
The solution to |x-3|-|x-3|-|x+4|<= 10 is True for all x