What is |3x-4|<= |x+4| ?

The solution to |3x-4|<= |x+4| is 0<= x<= 4

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|3x-4|<= |x+4|

∣ 3 x - 4 ∣ \leq ∣ x + 4 ∣

0 \leq x \leq 4

Interval Notation

[0, 4]

Solution steps

∣ 3 x - 4 ∣ \leq ∣ x + 4 ∣

Find positive and negative intervals

x < - 4, - 4 \leq x < \frac{4}{3}, x \geq \frac{4}{3}

Solve the inequality for each interval

No Solution or 0 \leq x < \frac{4}{3} or \frac{4}{3} \leq x \leq 4

Merge Overlapping Intervals

0 \leq x \leq 4

1 0^{\frac{3}{2}}

m^{2} + 10 m + 5 = - 11

\frac{m}{8} = \frac{15}{24}

∣ 4 x + 3 ∣ + 3 x \geq 1

\frac{4}{6}