11.3 Solving equations of the form x+a=b and x-a=b

Verify that 3 is a solution to ${\displaystyle x+7=\text{10}}$ .

When ${\displaystyle x=3}$ ,

${\displaystyle \begin{array}{ccccc}& \hfill x+7& =& 10\hfill & \\ \hfill \text{becomes}& \hfill 3+7& =& 10\hfill & \\ & \hfill 10& =& 10\hfill & \begin{array}{c}\text{which is a}\mathit{\text{ true }}\text{statement, verifying that}\hfill \\ 3\text{ is a solution to }x+7=10\hfill \end{array}\end{array}}$

Verify that ${\displaystyle -6}$ is a solution to ${\displaystyle 5y+8=-\text{22}}$

When ${\displaystyle y=-6}$ ,

${\displaystyle \begin{array}{ccccc}& \hfill 5y+8& =& -22\hfill & \\ \hfill \text{becomes}& \hfill 5(-6)+8& =& -22\hfill & \\ & \hfill -30+8& =& -22\hfill & \\ & \hfill -22& =& -22\hfill & \begin{array}{c}\text{which is a}\mathit{\text{ true }}\text{statement, verifying that}\hfill \\ -\mathrm{6 }\text{is a solution to}5y+8=-22\hfill \end{array}\end{array}}$

Verify that 5 is not a solution to ${\displaystyle a-1=2a+3}$ .

When ${\displaystyle a=5}$ ,

${\displaystyle \begin{array}{ccccc}& \hfill a-1& =& 2a+3\hfill & \\ \hfill \text{becomes}& \hfill 5-1& =& 2\cdot 5+3\hfill & \\ & \hfill 5-1& =& 10+3\hfill & \\ & \hfill 4& =& 13\hfill & \begin{array}{c}\text{a}\mathit{\text{ false }}\text{statement, verifying that }5\hfill \\ \text{ is not a solution to }a-1=2a+3\hfill \end{array}\hfill \end{array}}$

Verify that -2 is a solution to ${\displaystyle 3m-2=-4m-\text{16}}$ .

When ${\displaystyle m=-2}$ ,

${\displaystyle \begin{array}{ccccc}& \hfill 3m-2& =& -4m-16\hfill & \\ \hfill \text{becomes}& \hfill 3(-2)-2& =& -4(-2)-16\hfill & \\ & \hfill -6-2& =& 8-16\hfill & \\ & \hfill -8& =& -8\hfill & \begin{array}{c}\text{which is a }\mathit{\text{true}}\text{ statement, verifying that}\hfill \\ -2\text{ is a solution to }3m-2=-4m-16\hfill \end{array}\end{array}}$