What is the answer to |3-x|-|x+2|=5 ?

The answer to |3-x|-|x+2|=5 is x<=-2

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|3-x|-|x+2|=5

∣ 3 - x ∣ - ∣ x + 2 ∣ = 5

x \leq - 2

Solution steps

∣ 3 - x ∣ - ∣ x + 2 ∣ = 5

Find positive and negative intervals

x < - 2, - 2 \leq x \leq 3, x > 3

Solve the inequality for each interval

x < - 2 or x = - 2 or No Solution

Merge Overlapping Intervals

x \leq - 2

3 ∣ x + 2 ∣ = 4 x + 5

∣ x + 6 ∣ - 7 = - 3

- 3 ∣ 9 x + 6 ∣ - 10 = 73

∣ 2 x - 5 ∣ = ∣ 10 x - 9 ∣

x^{2} - 3 x = 4 x