What is |x-5|+|x-2|<= 7 ?

The solution to |x-5|+|x-2|<= 7 is 0<= x<= 7

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|x-5|+|x-2|<= 7

∣ x - 5 ∣ + ∣ x - 2 ∣ \leq 7

0 \leq x \leq 7

Interval Notation

[0, 7]

Solution steps

∣ x - 5 ∣ + ∣ x - 2 ∣ \leq 7

Find positive and negative intervals

x < 2, 2 \leq x < 5, x \geq 5

Solve the inequality for each interval

0 \leq x < 2 or 2 \leq x < 5 or 5 \leq x \leq 7

Merge Overlapping Intervals

0 \leq x \leq 7

- 8 x y^{3} (16 x^{5} y)

- 3 x^{2} + 16 x + 9 = - 2 x

224 - 54

7 x - 21

2 + (- 6)