What is the answer to |2b-9|=|b-6| ?

The answer to |2b-9|=|b-6| is b=3\lor b=5

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|2b-9|=|b-6|

∣ 2 b - 9 ∣ = ∣ b - 6 ∣

b = 3 or b = 5

Solution steps

∣ 2 b - 9 ∣ = ∣ b - 6 ∣

Find positive and negative intervals

b < \frac{9}{2}, \frac{9}{2} \leq b < 6, b \geq 6

Solve the inequality for each interval

b = 3 or b = 5 or No Solution

b = 3 or b = 5

∣ x - 2 ∣ \cdot + (x - 1) \cdot + (x + 1) \cdot + (x + 2) = 4

∣ - 2 x + 3 ∣ = ∣ 5 x - 1 ∣

∣ x ∣ + 2 = 11

∣ x + 4 ∣ = ∣ x - 8 ∣

∣ x + 1 ∣ + 2 ∣ x + 2 ∣ = x + 3