Given the equation 5 + x -12 = 2x – 7. Part A. Solve the equation 5 + x – 12 = 2x – 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 = 2x – 7 . In your final answer, include all of your calculations.
The Correct Answer and Explanation is:
Part A: Solve the equation
We are given the equation:
5+x−12=2x−75 + x – 12 = 2x – 75+x−12=2x−7
Step 1: Combine like terms on the left-hand side of the equation.
5−12+x=2x−75 – 12 + x = 2x – 75−12+x=2x−7
−7+x=2x−7-7 + x = 2x – 7−7+x=2x−7
Step 2: Move the terms involving xxx to one side by subtracting xxx from both sides.
−7=x−7-7 = x – 7−7=x−7
Step 3: To isolate xxx, add 7 to both sides.
0=x0 = x0=x
Thus, the solution to the equation is:
x=0x = 0x=0
Part B: Verify the solution using x=−0.5x = -0.5x=−0.5, x=0x = 0x=0, and x=1x = 1x=1
1. Test x=−0.5x = -0.5x=−0.5:
Substitute x=−0.5x = -0.5x=−0.5 into the original equation:
5+(−0.5)−12=2(−0.5)−75 + (-0.5) – 12 = 2(-0.5) – 75+(−0.5)−12=2(−0.5)−7
Simplify both sides:
5−0.5−12=−1−75 – 0.5 – 12 = -1 – 75−0.5−12=−1−7
−7.5=−8-7.5 = -8−7.5=−8
Since −7.5≠−8-7.5 \neq -8−7.5=−8, x=−0.5x = -0.5x=−0.5 is not a solution.
2. Test x=0x = 0x=0:
Substitute x=0x = 0x=0 into the original equation:
5+0−12=2(0)−75 + 0 – 12 = 2(0) – 75+0−12=2(0)−7
Simplify both sides:
5−12=0−75 – 12 = 0 – 75−12=0−7
−7=−7-7 = -7−7=−7
Since both sides are equal, x=0x = 0x=0 is a solution.
3. Test x=1x = 1x=1:
Substitute x=1x = 1x=1 into the original equation:
5+1−12=2(1)−75 + 1 – 12 = 2(1) – 75+1−12=2(1)−7
Simplify both sides:
6−12=2−76 – 12 = 2 – 76−12=2−7
−6=−5-6 = -5−6=−5
Since −6≠−5-6 \neq -5−6=−5, x=1x = 1x=1 is not a solution.
Conclusion:
The solution to the equation is x=0x = 0x=0. The only value that satisfies the equation is x=0x = 0x=0, as shown by the verification steps.
