What is the answer to |X-5|+|X+2|=7 ?

The answer to |X-5|+|X+2|=7 is -2<= X<= 5

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|X-5|+|X+2|=7

∣ X - 5 ∣ + ∣ X + 2 ∣ = 7

- 2 \leq X \leq 5

Solution steps

∣ X - 5 ∣ + ∣ X + 2 ∣ = 7

Find positive and negative intervals

X < - 2, - 2 \leq X < 5, X \geq 5

Solve the inequality for each interval

No Solution or - 2 \leq X < 5 or X = 5

Merge Overlapping Intervals

- 2 \leq X \leq 5

∣ y ∣ + 6 = 12

\frac{1}{2} x - 2 = 14

x^{2} - 7 x = 12

∣ 2 x ∣ = - 7

∣ x + 3 ∣ + ∣ x - 1 ∣ = 6