What is the answer to |x-2|+|x+2|=4 ?

The answer to |x-2|+|x+2|=4 is -2<= x<= 2

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|x-2|+|x+2|=4

∣ x - 2 ∣ + ∣ x + 2 ∣ = 4

- 2 \leq x \leq 2

Solution steps

∣ x - 2 ∣ + ∣ x + 2 ∣ = 4

Find positive and negative intervals

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

Solve the inequality for each interval

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

Merge Overlapping Intervals

- 2 \leq x \leq 2

∣ 5 x - 2 ∣ - 5 = 0

\frac{2 \frac{2}{3} - x + 1}{4} = \frac{3}{4}

x, 3 ∣ y - 2 ∣ + 5 (2 x - y + 1)^{2} = 0

3 ∣ x ∣ + 2 = 8

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