Question

match each equation with the term that describes it. keyboard help 10 - m = m - 10 7x + 5 = 7(x + 5) 3(t + 2) = (2 + 3t) + 4 one solution no solution identity

Explanation:

Step1: Solve first equation

Start with $10 - m = m - 10$.
Add $m$ to both sides: $10 = 2m - 10$.
Add 10 to both sides: $20 = 2m$.
Divide by 2: $m = 10$.
This has one unique solution.

Step2: Solve second equation

Start with $7x + 5 = 7(x + 5)$.
Expand right side: $7x + 5 = 7x + 35$.
Subtract $7x$ from both sides: $5 = 35$.
This is a false statement, so no solution.

Step3: Solve third equation

Start with $3(t + 2) = (2 + 3t) + 4$.
Expand left side: $3t + 6 = 2 + 3t + 4$.
Simplify right side: $3t + 6 = 3t + 6$.
This is true for all $t$, so it is an identity.

Answer:

1. $10 - m = m - 10$ → one solution
2. $7x + 5 = 7(x + 5)$ → no solution
3. $3(t + 2) = (2 + 3t) + 4$ → identity