Given the equation
5
+
x
−
12
=
2
x
−
7
:
Part A. Solve the equation
5
+
x
−
12
=
2
x
−
7
. In your final answer, be sure to state the solution and include all of your work.
Part B. Use the values
x
=
−
0.5
,
0
,
1
to prove your solution to the equation
5
+
x
−
12
=
2
x
−
7
. In your final answer, include all of your calculations.
Part A. Solve the equation:
Step 1: Simplify the equation by combining like terms on the left side:
5 + x - 12 = 2x - 7
x - 7 = 2x - 7
Step 2: Subtract x from both sides of the equation:
-7 = x - 7
Step 3: Add 7 to both sides of the equation to isolate x:
x = 0
Solution: x = 0
Part B. Test the solution by plugging in x = -0.5, 0, and 1 into the equation:
For x = -0.5:
5 + (-0.5) - 12 = 2(-0.5) - 7
-7.5 = -8 + 0.5
-7.5 ≠ -7.5
For x = 0:
5 + 0 - 12 = 2(0) - 7
-7 = -7 (True)
For x = 1:
5 + 1 - 12 = 2(1) - 7
-6 = -5 + 2
-6 ≠ -3
The values x = -0.5 and x = 1 do not satisfy the equation, but x = 0 does, which confirms our solution.