What is |x+3|>|2x-4| ?

The solution to |x+3|>|2x-4| is 1/3 <x<7

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|x+3|>|2x-4|

∣ x + 3 ∣ > ∣ 2 x - 4 ∣

\frac{1}{3} < x < 7

Interval Notation

(\frac{1}{3}, 7)

Decimal Notation

0.33333 \dots < x < 7

Solution steps

∣ x + 3 ∣ > ∣ 2 x - 4 ∣

Find positive and negative intervals

x < - 3, - 3 \leq x < 2, x \geq 2

Solve the inequality for each interval

No Solution or \frac{1}{3} < x < 2 or 2 \leq x < 7

Merge Overlapping Intervals

\frac{1}{3} < x < 7

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

(b) ∣ 1 - x ∣ < ∣ 4 + x ∣

∣ 5 p + 2 ∣ < - 4

∣ 3 - 4 x ∣ > 5

\frac{1}{( ∣ x ∣ - 3 )} \leq \frac{1}{2}