x−7=7−x
one solution
two solutions
no solutions
infinite solutions
This equation simplifies to 2x - 7 = 7, which further simplifies to 2x = 14. Dividing both sides by 2, we get x = 7. Therefore, there is one solution to the equation.
To determine the number of solutions to the equation x - 7 = 7 - x, we can simplify and solve for x.
Step 1: Distribute the negative sign on the second term:
x - 7 = 7 + (-x)
Step 2: Combine like terms:
x - 7 = 7 - x
Step 3: Add x to both sides of the equation:
x + x - 7 = 7 - x + x
2x - 7 = 7
Step 4: Add 7 to both sides of the equation:
2x - 7 + 7 = 7 + 7
2x = 14
Step 5: Divide both sides of the equation by 2:
(2x)/2 = 14/2
x = 7
The simplified equation is x = 7. This equation has only one solution. Therefore, the answer is "one solution".