Question

consider the equation: 10b+18=38, add 4 to each side of the equation. Tell how you know that the two sides of the equation are still equal

Answer 1

When we add 4 to each side of the equation, we are applying the addition property of equality:

$a=b\Rightarrow a+c=b+c$

We can prove this by solving the orginal equation for b, and then solving it again after adding 4 to each side:

Original:

$\begin{gathered} 10b+18=38 \\ 10b=38-18 \\ 10b=20 \\ b=\frac{20}{10} \\ b=2 \end{gathered}$

After addition:

$\begin{gathered} 10b+18+4=38+4 \\ 10b+22=42 \\ 10b=42-22 \\ 10b=20 \\ b=\frac{20}{10} \\ b=2 \end{gathered}$

The result is the same for both, confirming what the addition property tells.