What is |x-2|-|x+6|<= 3 ?

The solution to |x-2|-|x+6| =-7/2

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|x-2|-|x+6|<= 3

∣ x - 2 ∣ - ∣ x + 6 ∣ \leq 3

x \geq - \frac{7}{2}

Solution steps

∣ x - 2 ∣ - ∣ x + 6 ∣ \leq 3

Find positive and negative intervals

x < - 6, - 6 \leq x < 2, x \geq 2

Solve the inequality for each interval

No Solution or - \frac{7}{2} \leq x < 2 or x \geq 2

Merge Overlapping Intervals

x \geq - \frac{7}{2}

3 x - 1 < 0

0 \leq x \leq 4

x^{2} - 12 x + 2 = 0

2 x^{2} + 22 x + 36

(- 2 + 6 i) + (4 - i)