What is |x+5|>= |5x-7| ?

The solution to |x+5|>= |5x-7| is 1/3 <= x<= 3

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|x+5|>= |5x-7|

∣ x + 5 ∣ \geq ∣ 5 x - 7 ∣

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

Interval Notation

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

Decimal Notation

0.33333 \dots \leq x \leq 3

Solution steps

∣ x + 5 ∣ \geq ∣ 5 x - 7 ∣

Find positive and negative intervals

x < - 5, - 5 \leq x < \frac{7}{5}, x \geq \frac{7}{5}

Solve the inequality for each interval

No Solution or \frac{1}{3} \leq x < \frac{7}{5} or \frac{7}{5} \leq x \leq 3

Merge Overlapping Intervals

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

1 - \frac{x - 2}{x} < - 3

∣ x + 1 ∣ > x - 3

∣ 2 x - 3 ∣ < x + 1

x^{2} - 4 x < 5, ∣ x + 1 ∣ < 3

\frac{( 3 x )}{4 - 2} < 8