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

The answer to |3x-2|=|x-3| is x=-1/2 \lor x= 5/4

Solve for x: |3x-2|=|x-3|

The solution is x=-1/2 \lor x= 5/4

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∣ 3 x - 2 ∣ = ∣ x - 3 ∣

x = - \frac{1}{2} or x = \frac{5}{4}

Decimal Notation

x = - 0.5, x = 1.25

Solution steps

∣ 3 x - 2 ∣ = ∣ x - 3 ∣

Find positive and negative intervals

x < \frac{2}{3}, \frac{2}{3} \leq x < 3, x \geq 3

Solve the inequality for each interval

x = - \frac{1}{2} or x = \frac{5}{4} or No Solution

x = - \frac{1}{2} or x = \frac{5}{4}

∣ x - 1 ∣ = - 3 x

2 \cdot ∣ x - 2 ∣ - 3 \cdot ∣ 2 x + 4 ∣ = 5 - 2 \cdot (1 - 3 x)

∣ 2 x - 1 ∣ = x + 1

x^{2} - 1 + ∣ x ∣ = 2

3 - 2 ∣ x + 1 ∣ = 1

What is the answer to |3x-2|=|x-3| ?
The answer to |3x-2|=|x-3| is x=-1/2 \lor x= 5/4
Solve for x: |3x-2|=|x-3|
The solution is x=-1/2 \lor x= 5/4