Question

Solve the equation:
-10+7 |4x-8|=46

Answer 1

To solve the given equation, isolate the absolute value expression and consider both the positive and negative scenarios. Simplifying these gives two solutions: x = 4 and x = 0.

Step-by-step explanation:

To solve the equation -10 + 7 |4x - 8| = 46, let's isolate the absolute value term.

1. Add 10 to both sides to get 7 |4x - 8| = 56.
2. Divide both sides by 7 to get |4x - 8| = 8.
3. Now we have two possible scenarios, since the absolute value of an expression can be either positive or negative:

• Case 1: 4x - 8 = 8. Adding 8 to both sides yields 4x = 16, and then dividing by 4 gives x = 4.
• Case 2: 4x - 8 = -8. Adding 8 to both sides yields 4x = 0, and then dividing by 4 gives x = 0.

Check both solutions to ensure they fit the original equation.

The solutions are x = 4 and x = 0.