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
−
7
. In your final answer, include all of your calculations.
Part A:
5 + x - 12 = x - 7
Simplifying by combining like terms:
x - 7 = x - 7
Subtracting x from both sides:
-7 = -7
Therefore, the equation has infinitely many solutions. Any value of x will satisfy the equation.
Part B:
Using x = -4:
5 + (-4) - 12 = (-4) - 7
-11 = -11
The equation holds true for x = -4.
Using x = 0:
5 + 0 - 12 = 0 - 7
-7 = -7
The equation holds true for x = 0.
Using x = 5:
5 + 5 - 12 = 5 - 7
-2 ≠ -2
The equation does not hold true for x = 5.
Therefore, since the equation only holds true for x = -4 and x = 0, these are the solutions to the equation.