What is |2x-5|<= |x+4| ?

The solution to |2x-5|<= |x+4| is 1/3 <= x<= 9

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|2x-5|<= |x+4|

∣ 2 x - 5 ∣ \leq ∣ x + 4 ∣

\frac{1}{3} \leq x \leq 9

Interval Notation

[\frac{1}{3}, 9]

Decimal Notation

0.33333 \dots \leq x \leq 9

Solution steps

∣ 2 x - 5 ∣ \leq ∣ x + 4 ∣

Find positive and negative intervals

x < - 4, - 4 \leq x < \frac{5}{2}, x \geq \frac{5}{2}

Solve the inequality for each interval

No Solution or \frac{1}{3} \leq x < \frac{5}{2} or \frac{5}{2} \leq x \leq 9

Merge Overlapping Intervals

\frac{1}{3} \leq x \leq 9

21 x - 15 y

\frac{- 2}{9}

(x - 5) (x + 2) = 0

\frac{a}{a ^{5}}

- \frac{3}{2} \cdot 2