Problem
We want to solve the equation:
15 = \'\frac{1}{2} - 11
First, notice this equation does not contain a variable. It is a statement comparing numbers, and it is not true as written because \(\frac{1}{2} - 11 = -\tfrac{21}{2} = -10.5\), which does not equal 15.
There might be a misunderstanding of the problem. If the intent is to solve a linear equation in one variable, it should look like something like:
- case A: 15 = x/2 - 11
- case B: 15 = 1/2 - x
We’ll show how to handle case A, since it fits the pattern of solving for a variable.
Solving Case A: 15 = x/2 - 11
- Add 11 to both sides to move constants:
15 + 11 = x/2
26 = x/2
- Multiply both sides by 2 to solve for x:
2 × 26 = x
x = 52
- Check the solution by substituting back:
Right side: x/2 - 11 = 52/2 - 11 = 26 - 11 = 15
Left side is 15, which matches. So x = 52 is correct for Case A.
Important note: If your original problem is truly 15 = 1/2 - 11 (with no variable), that equality is false because 1/2 - 11 = -10.5. There is no solution to solve for a variable because none appears. Please double-check the equation you were given. If you intended a variable, use a form like 15 = x/2 - 11 or 15 = 1/2 - x and solve accordingly.