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

The solution to |x+2|+|x|<= 3 is -5/2 <= x<= 1/2

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|x+2|+|x|<= 3

∣ x + 2 ∣ + ∣ x ∣ \leq 3

- \frac{5}{2} \leq x \leq \frac{1}{2}

Solution steps

∣ x + 2 ∣ + ∣ x ∣ \leq 3

Find positive and negative intervals

x < - 2, - 2 \leq x < 0, x \geq 0

Solve the inequality for each interval

- \frac{5}{2} \leq x < - 2 or - 2 \leq x < 0 or 0 \leq x \leq \frac{1}{2}

Merge Overlapping Intervals

- \frac{5}{2} \leq x \leq \frac{1}{2}

- 3 x - 5 < 10

6 x + 6 = 24

lo g_{e} (10)

98 x^{2} - 200 y^{2}

\frac{1}{2} y + 6 = 4