What is 5<|2x-5|<= 9 ?

The solution to 5<|2x-5|<= 9 is -2<= x<0\lor 5<x<= 7

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5<|2x-5|<= 9

5 < ∣ 2 x - 5 ∣ \leq 9

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

Interval Notation

[- 2, 0) \cup (5, 7]

Solution steps

5 < ∣ 2 x - 5 ∣ \leq 9

a < u \leq b

then

a < u and u \leq b

5 < ∣ 2 x - 5 ∣ and ∣ 2 x - 5 ∣ \leq 9

5 < ∣ 2 x - 5 ∣ : x < 0 or x > 5

∣ 2 x - 5 ∣ \leq 9 : - 2 \leq x \leq 7

Combine the intervals

(x < 0 or x > 5) and - 2 \leq x \leq 7

Merge Overlapping Intervals

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

140 ab - 60 a^{2} + 168 b - 72 a

x^{2} (x + 4) - 8 x (x + 4) + 16 (x + 4)

\frac{1}{2} + \frac{2}{2}

(2 i)^{2} - i (- 2 - i) + 5 - 2 i

5 x + 12 + 3 x = 8 x - 5