What is |x-1|+|x+3|-|x-2|<= 4 ?

The solution to |x-1|+|x+3|-|x-2|<= 4 is -8<= x<= 4/3

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|x-1|+|x+3|-|x-2|<= 4

∣ x - 1 ∣ + ∣ x + 3 ∣ - ∣ x - 2 ∣ \leq 4

- 8 \leq x \leq \frac{4}{3}

Interval Notation

[- 8, \frac{4}{3}]

Decimal Notation

- 8 \leq x \leq 1.33333 \dots

Solution steps

∣ x - 1 ∣ + ∣ x + 3 ∣ - ∣ x - 2 ∣ \leq 4

Find positive and negative intervals

x < - 3, - 3 \leq x < 1, 1 \leq x < 2, x \geq 2

Solve the inequality for each interval

- 8 \leq x < - 3 or - 3 \leq x < 1 or 1 \leq x \leq \frac{4}{3} or No Solution

Merge Overlapping Intervals

- 8 \leq x \leq \frac{4}{3}

8 x^{2} - 37 x - 15

m^{2} + 5 m + 6

x^{2} + 2 x + 5 x + 10

w^{2} - 144

3 x^{2} = 4 x - x^{2}

What is |x-1|+|x+3|-|x-2|<= 4 ?
The solution to |x-1|+|x+3|-|x-2|<= 4 is -8<= x<= 4/3