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

The solution to |2x+3|<= x+3 is -2<= x<= 0

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|2x+3|<= x+3

∣ 2 x + 3 ∣ \leq x + 3

- 2 \leq x \leq 0

Interval Notation

[- 2, 0]

Solution steps

∣ 2 x + 3 ∣ \leq x + 3

Find positive and negative intervals

x < - \frac{3}{2}, x \geq - \frac{3}{2}

Solve the inequality for each interval

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

Merge Overlapping Intervals

- 2 \leq x \leq 0

12 - 5 (x + 3) = 4 x - 5

- \frac{60}{50}

36 n^{2} - 18 n - 45

\frac{4 ^{- 1} + 2 ^{- 2}}{2 ^{- 3}}

3 x^{6} y^{2} + 81 y^{2}