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-7In your final answer, include all of your calculations.
Part A.
To solve the equation 5+x-14=x-7, first combine the constants on one side of the equation.
5 - 14 = -9,
so the equation is now x - 9 = x - 7.
To isolate x, subtract x from both sides of the equation:
x - x - 9 = x - x - 7
-9 = -7
However, this statement is false, as -9 is not equal to -7. Therefore, there is no solution to the equation 5+x-14=x-7.
Part B.
Since there is no solution to the equation, no matter what value of x we choose, the equation will not hold true. To demonstrate this, plug in the given values for x:
x = -2:
5 + (-2) - 14 = (-2) - 7
3 - 14 = -9
-11 ≠ -9
x = 0:
5 + (0) - 14 = (0) - 7
5 - 14 = -7
-9 ≠ -7
x = 3:
5 + (3) - 14 = (3) - 7
8 - 14 = -4
-6 ≠ -4
In all three cases, the equation doesn't hold true. This further verifies that there is no solution to the equation 5+x-14=x-7.