Given the equation
5
+
x
−
14
=
x
−
7
:
Part A. Solve the equation
5
+
x
−
14
=
x
−
7
. In your final answer, be sure to state the solution and include all of your work.
Part B. Use the values
x
=
−
2
,
0
,
3
to verify your solution to the equation
5
+
x
−
14
=
x
−
7
. In your final answer, include all of your calculations.
Part A:
To solve the equation, first simplify it:
5 + x - 14 = x - 7
-9 + x = x - 7
Now, subtract x from both sides of the equation:
-9 = -7
This equation is not true, so there is no solution for x.
Part B:
If we plug in the values of x = -2, 0, and 3 into the equation 5 + x - 14 = x - 7, let's see if any of them would make the equation true:
For x = -2:
5 + (-2) - 14 ≠ (-2) - 7
-11 ≠ -9
The equation is false.
For x = 0:
5 + 0 - 14 ≠ 0 - 7
-9 ≠ -7
The equation is false.
For x = 3:
5 + 3 - 14 ≠ 3 - 7
-6 ≠ -4
The equation is false.
None of the given values of x make the equation true, which verifies our finding that there is no solution for this equation.