Question

Solve the absolute value equ 3|2x-1|=21

Answer 1

To solve the absolute value equation 3|2x-1|=21, divide both sides by 3, and consider the two cases of the absolute value expression, resulting in the solutions x = 4 or x = -3.

Step-by-step explanation:

To solve the absolute value equation 3|2x-1|=21, we can start by isolating the absolute value expression on one side of the equation by dividing both sides by 3, resulting in |2x-1| = 7. Next, we consider the two cases that make the absolute value true:

1. 2x - 1 = 7
2. 2x - 1 = -7

For the first case, adding 1 to both sides gives us 2x = 8, and then dividing both sides by 2 gives us x = 4.

For the second case, adding 1 to both sides gives us 2x = -6, and then dividing both sides by 2 gives us x = -3.

Therefore, the solution to the equation is x = 4 or x = -3.