To solve equations with variables, we use inverse operations.
Inverse operations are operations that cancel each other out.
(plus and minus, multiply and divide)
Say we had \(x-3=6\).
According to the addition property of equality, we could add 3 to each side of that equation and it would still be equal.
\(x-3+3=6+3\)
This would cancel out the -3 and leave us with just \(x=9\).
Question 1) Solve \(2(n-7)+3=9\).
Let's just start cancelling things out. Doesn't matter what order.
\(2(n-7)+3=9 \\ 2(n-7)+3-3=9-3\\ 2(n-7)=6 \\\\\ \frac{2(n-7)}2=\frac{6}2\
-7=3\\\
-7+7=3+7\\\boxed{n=10}\)
Question 2) Solve \(4h+7h-16=6\).
You can add \(4h\) and \(7h\) together to get \(11h\). The h acts sort of like a unit in that case, like 4 feet + 7 feet = 11 feet.
\(11h-16=6\\11h-16+16=6+16\\11h=22\\\\\frac{11h}{11}=\frac{22}{11}\\\boxed{h=2}\)
