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

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

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|x+3|<= |x|

∣ x + 3 ∣ \leq ∣ x ∣

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

Interval Notation

(- \infty, - \frac{3}{2}]

Decimal Notation

x \leq - 1.5

Solution steps

∣ x + 3 ∣ \leq ∣ x ∣

Find positive and negative intervals

x < - 3, - 3 \leq x < 0, x \geq 0

Solve the inequality for each interval

x < - 3 or - 3 \leq x \leq - \frac{3}{2} or No Solution

Merge Overlapping Intervals

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

8 k - (6 k - 4) = 10

(x - 3 y) (3 x + 5 y) - (3 x + 5 y) (x + 2 y)

2 (3 y - 7) = 16

2 x^{2} + 4 x = x^{2} - 3 x - 15

\frac{y - 9}{2} < - 4