Question

Equation or indicate that equation has no solution. 7|2x-3|=21

Answer 1

To solve the equation 7|2x-3|=21, divide both sides by 7 and solve each case separately for the absolute value expression.

Step-by-step explanation:

To solve the equation 7|2x-3|=21, we need to isolate the absolute value expression and then solve for x. Here are the steps:

1. Divide both sides of the equation by 7: |2x-3|=3
2. Now we have two possible cases: 2x-3=3 or 2x-3=-3
3. Solve each case separately:
   • If 2x-3=3, add 3 to both sides to get 2x=6 and divide by 2 to find x=3
   • If 2x-3=-3, add 3 to both sides to get 2x=0 and divide by 2 to find x=0
4. So the equation has two solutions: x=3 and x=0