What is |x+2|+|x|<= 5 ?

The solution to |x+2|+|x|<= 5 is -7/2 <= x<= 3/2

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|x+2|+|x|<= 5

∣ x + 2 ∣ + ∣ x ∣ \leq 5

- \frac{7}{2} \leq x \leq \frac{3}{2}

Interval Notation

[- \frac{7}{2}, \frac{3}{2}]

Decimal Notation

- 3.5 \leq x \leq 1.5

Solution steps

∣ x + 2 ∣ + ∣ x ∣ \leq 5

Find positive and negative intervals

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

Solve the inequality for each interval

- \frac{7}{2} \leq x < - 2 or - 2 \leq x < 0 or 0 \leq x \leq \frac{3}{2}

Merge Overlapping Intervals

- \frac{7}{2} \leq x \leq \frac{3}{2}

3 x^{2} \cdot x^{2}

\frac{x}{2} = \frac{8}{9}

x^{3} + 8 x^{2} + 9 x - 18

5 x - 4 = 3 x - 6

- 2 (7 + y) \geq - 8 (y + 1)