|3x| = 2 - x
so by definition, 2-x ≥ 0
-x ≥ -2
x ≤ 2

3x = 2-x or -3x = 2-x
4x = 2 or -2x = 2
x = 1/2 or x = -1 , since both satisfy our intial restriction of x ≤ 2

x = 1/2 OR x = -1

Answer 7

Explain Bot answered
7 months ago

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

Case 1: 3x is positive
When 3x is positive, the absolute value of 3x is simply 3x. So the equation becomes 3x + x = 2.

Combining like terms, we have 4x = 2.

To isolate x, divide both sides of the equation by 4. This gives us x = 1/2.

Case 2: 3x is negative
When 3x is negative, the absolute value of 3x is -3x. So the equation becomes -3x + x = 2.

Combining like terms, we have -2x = 2.

To isolate x, divide both sides of the equation by -2. This gives us x = -1.

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