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 ∣ \geq 7 - x

x \leq 1 or x \geq 4

Interval Notation

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

Solution steps

∣ 4 - x ∣ + ∣ 2 x - 5 ∣ \geq 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 \leq 1 or x = 4 or x > 4

Merge Overlapping Intervals

x \leq 1 or x \geq 4

h^{2} + 48 = 16 h

2 a^{2} + 7 ab - 15 b^{2}

200 \cdot \frac{π}{12} \cdot \frac{1.16}{1.3} \cdot 5

2 i z + \frac{2 i}{1 - i} = 4 i

4 x + 3 = 11

What is |4-x|+|2x-5|>= 7-x ?
The solution to |4-x|+|2x-5|>= 7-x is x<= 1\lor x>= 4