Final answer:
To solve the equation 3/5(x - 4) = 12, multiply both sides by the reciprocal of the fraction and then add 4 to both sides to solve for x, which results in x = 24.
Step-by-step explanation:
To solve the equation 3/5 (x - 4) = 12 using inverse operations, follow these steps:
- First, you want to isolate the variable x. To do this, start by undoing the multiplication of 3/5. Multiply both sides of the equation by the reciprocal of 3/5, which is 5/3, to get:
- 5/3 * 3/5 (x - 4) = 5/3 * 12
- On the left side, the 5/3 and 3/5 cancel each other out, leaving you with:
- x - 4 = 20
- Next, you need to get x by itself by getting rid of the -4. Add 4 to both sides of the equation:
- x - 4 + 4 = 20 + 4
- Finally, simplify to find the solution:
- x = 24
You have successfully solved for x using inverse operations.