What is |4-x|+|2x-5|>7-x ?

The solution to |4-x|+|2x-5|>7-x is x 4

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|4-x|+|2x-5|>7-x

∣ 4 - x ∣ + ∣ 2 x - 5 ∣ > 7 - x

x < 1 or x > 4

Interval Notation

(- \infty, 1) \cup (4, \infty)

Solution steps

∣ 4 - x ∣ + ∣ 2 x - 5 ∣ > 7 - x

Find positive and negative intervals

x < \frac{5}{2}, \frac{5}{2} \leq x \leq 4, x > 4

Solve the inequality for each interval

x < 1 or No Solution or x > 4

Merge Overlapping Intervals

x < 1 or x > 4

v^{2} + 14 v + 13

6 y^{2} + 41 y + 13

7 x^{2} - 13 x - 1 = 0

4 x^{2} + 8 x + 20 = 0

2 x^{4} - 7 x^{3} + 3 x^{2} + 8 x - 4