Question

Solve |3x - 4|= 6
1. {-2/3, 10/3}
2.{ -2/3, 2/3}
3.{ -10/3,10/3}

Answer 1

The absolute value equation \(|3x - 4| = 61\) is solved by setting up two separate equations for when the inside is positive and negative, yielding solutions x = 21.67 and x = -19, which do not match the provided options.

Step-by-step explanation:

The student is asked to solve the absolute value equation \(|3x - 4| = 61\). To solve this, we must consider both the positive and negative scenarios because the absolute value of a number is its distance from zero on the number line, without considering direction.

We set up two separate equations, removing the absolute value:

1. If the expression inside the absolute value is positive: 3x - 4 = 61. Solving for x, we add 4 to both sides, getting 3x = 65, and then divide by 3, so x = 65/3 or x = 21.67.
2. If the expression inside the absolute value is negative: -(3x - 4) = 61, or 3x - 4 = -61. Solving for x, we add 4 to both sides to get 3x = -57 and then divide by 3, resulting in x = -57/3 or x = -19.

Therefore, the solutions to the given absolute value equation are x = 21.67 and x = -19. However, these solutions do not match the options provided in the question, which suggests there may have been a typo or misunderstanding in the original problem.