Question

|3х-1|=2 решите уравнение ​

Answer 1

$|3 x - 1 | = 2 \\ \\ \\ 3x - 1 = 2 \\ 3x - 1 = - 2 \\ \\ \\ 3x = 3 \\ 3x = - 1 \\ \\ \\ x_{1} = 1. \\ x_{2}= - \frac{1}{3} .$

Answer 2

To solve the equation |3x - 1| = 2, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: 3x - 1 > 0 In this case, the absolute value simplifies to 3x - 1, so we have: 3x - 1 = 2

Solving for x: 3x = 2 + 1 3x = 3 x = 3/3 x = 1

So x = 1 is a solution for this case.

Case 2: 3x - 1 < 0 In this case, the absolute value simplifies to -(3x - 1), so we have: -(3x - 1) = 2

Solving for x: -3x + 1 = 2 -3x = 2 - 1 -3x = 1 x = 1/(-3) x = -1/3

So x = -1/3 is a solution for this case.

Therefore, the solutions to the equation |3x - 1| = 2 are x = 1 and x = -1/3.