Mikayla and Jesse both solved the equation x−15=12−8, using substitution. Mikayla says the answer is x=19, and Jesse says the answer is x=27. Which student is correct, and how do you know? Show your work and explain your thinking.
To solve x−15=12−8 using substitution, we need to replace the expression 12−8 with its value, which is 4.
Mikayla substituted 4 for 12−8 correctly and solved the equation as follows:
x−15=4
x=19
Therefore, Mikayla is correct.
Jesse substituted 4 for 12−8 correctly, but made an error in solving the equation:
x−15=4
x=27
Therefore, Jesse is incorrect.
We know this because we can substitute each answer back into the original equation and see which one makes it true:
For Mikayla's answer:
x−15=12−8
19−15=12−8
4=4
The equation is true, so Mikayla's answer is correct.
For Jesse's answer:
x−15=12−8
27−15=12−8
12=4
The equation is false, so Jesse's answer is incorrect.
In conclusion, Mikayla is correct and Jesse is incorrect.