What is |5x-2|<= |3x+5| ?

The solution to |5x-2|<= |3x+5| is -3/8 <= x<= 7/2

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|5x-2|<= |3x+5|

∣ 5 x - 2 ∣ \leq ∣ 3 x + 5 ∣

- \frac{3}{8} \leq x \leq \frac{7}{2}

Interval Notation

[- \frac{3}{8}, \frac{7}{2}]

Decimal Notation

- 0.375 \leq x \leq 3.5

Solution steps

∣ 5 x - 2 ∣ \leq ∣ 3 x + 5 ∣

Find positive and negative intervals

x < - \frac{5}{3}, - \frac{5}{3} \leq x < \frac{2}{5}, x \geq \frac{2}{5}

Solve the inequality for each interval

No Solution or - \frac{3}{8} \leq x < \frac{2}{5} or \frac{2}{5} \leq x \leq \frac{7}{2}

Merge Overlapping Intervals

- \frac{3}{8} \leq x \leq \frac{7}{2}

∣ x + 3 ∣ > ∣ 2 x - 4 ∣

\frac{2}{( x + 3 )} \leq 1

(b) ∣ 1 - x ∣ < ∣ 4 + x ∣

∣ 5 p + 2 ∣ < - 4

∣ 3 - 4 x ∣ > 5