Given the equation 5+x-12=x-7:Part A. Solve the equation 5+x-12=x-7. In your final answer, be sure to state the solution and include all of your work.
Part B. Use the values x=-4,0,5 to verify your solution to the equation 5+x-12=x-7In your final answer, include all of your calculations.
Part A: To solve the equation 5+x-12=x-7, we first simplify it by combining like terms.
5 - 12 = -7
So, the equation becomes -7+x=x-7.
Now, to solve for x, we'll subtract x from both sides of the equation:
-7 = -7 + x - x
-7 = -7
Since the equation ended up being a true statement (-7=-7), this means the original equation is an identity. There are infinitely many solutions because any value of x will satisfy the equation.
Part B: To verify our solution, we can try the suggested values of x (-4, 0, and 5) in the original equation:
For x = -4:
5 + (-4) - 12 = -4 - 7
-11 = -11 (True)
For x = 0:
5 + 0 - 12 = 0 - 7
-7 = -7 (True)
For x = 5:
5 + 5 - 12 = 5 -7
-2 = -2 (True)
As we can see, each of the given values of x result in true statements for the equation, further indicating that there are infinitely many solutions for this equation.