What is |2x+4.5|>|x-2.7| ?

The solution to |2x+4.5|>|x-2.7| is x -0.6

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|2x+4.5|>|x-2.7|

∣ 2 x + 4.5 ∣ > ∣ x - 2.7 ∣

x < - 7.2 or x > - 0.6

Interval Notation

(- \infty, - 7.2) \cup (- 0.6, \infty)

Solution steps

∣ 2 x + 4.5 ∣ > ∣ x - 2.7 ∣

Find positive and negative intervals

x < - 2.25, - 2.25 \leq x < 2.7, x \geq 2.7

Solve the inequality for each interval

x < - 7.2 or - 0.6 < x < 2.7 or x \geq 2.7

Merge Overlapping Intervals

x < - 7.2 or x > - 0.6

x, f > - ∣ x - 2 ∣ + 4

(a) ∣ x - 2 ∣ \leq ∣ x + 4 ∣

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

2 x^{2} - 5 x + 1 \geq 2

∣ x ∣ + ∣ 2 x - 8 ∣ \leq ∣ x + 8 ∣

What is |2x+4.5|>|x-2.7| ?
The solution to |2x+4.5|>|x-2.7| is x<-7.2\lor x>-0.6