What is the answer to 6|2x-3|-9=33 ?

The answer to 6|2x-3|-9=33 is x=-2\lor x=5

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6|2x-3|-9=33

6 ∣ 2 x - 3 ∣ - 9 = 33

x = - 2 or x = 5

Solution steps

6 ∣ 2 x - 3 ∣ - 9 = 33

Move

9

to the right side

6 ∣ 2 x - 3 ∣ = 42

Divide both sides by

6

∣ 2 x - 3 ∣ = 7

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

2 x - 3 = - 7 or 2 x - 3 = 7

2 x - 3 = - 7 or 2 x - 3 = 7

x = - 2 or x = 5

∣ x - 2 ∣ = 6 x + 18

10 - 2 ∣ x + 2 ∣ = 5

4 ∣ x - 6 ∣ + 2 = 30

5 ∣ x - 3 ∣ - 12 = 8

\frac{2}{7} ∣ - x - 3 ∣ = 2