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The following are examples of equations:
$\underset{\text{expression}}{\underset{\text{This}}{\underbrace{x+6}}}\underset{=}{\underset{}{\underset{}{=}}}\underset{\text{expression}}{\underset{\text{This}}{\underbrace{10}}}$ $\underset{\text{expression}}{\underset{\text{This}}{\underbrace{x-4}}}\underset{=}{\underset{}{\underset{}{=}}}\underset{\text{expression}}{\underset{\text{This}}{\underbrace{-11}}}$ $\underset{\text{expression}}{\underset{\text{This}}{\underbrace{3y-5}}}\underset{=}{\underset{}{\underset{}{=}}}\underset{\text{expression}}{\underset{\text{This}}{\underbrace{-2+2y}}}$
Notice that $x+6$ , $x-4$ , and $3y-5$ are not equations. They are expressions. They are not equations because there is no statement that each of these expressions is equal to another expression.
Verify that 3 is a solution to $x+7=\text{10}$ .
When $x=3$ ,
$\begin{array}{ccccc}& \hfill x+7& =& 10\hfill & \\ \hfill \text{becomes}& \hfill 3+7& =& 10\hfill & \\ & \hfill 10& =& 10\hfill & \begin{array}{c}\text{which is a}\mathit{\text{true}}\text{statement, verifying that}\hfill \\ 3\text{is a solution to}x+7=10\hfill \end{array}\end{array}$
Verify that $-6$ is a solution to $5y+8=-\text{22}$
When $y=-6$ ,
$\begin{array}{ccccc}& \hfill 5y+8& =& -22\hfill & \\ \hfill \text{becomes}& \hfill 5(-6)+8& =& -22\hfill & \\ & \hfill -30+8& =& -22\hfill & \\ & \hfill -22& =& -22\hfill & \begin{array}{c}\text{which is a}\mathit{\text{true}}\text{statement, verifying that}\hfill \\ -6\text{is a solution to}5y+8=-22\hfill \end{array}\end{array}$
Verify that 5 is not a solution to $a-1=2a+3$ .
When $a=5$ ,
$\begin{array}{ccccc}& \hfill a-1& =& 2a+3\hfill & \\ \hfill \text{becomes}& \hfill 5-1& =& 2\cdot 5+3\hfill & \\ & \hfill 5-1& =& 10+3\hfill & \\ & \hfill 4& =& 13\hfill & \begin{array}{c}\text{a}\mathit{\text{false}}\text{statement, verifying that}5\hfill \\ \text{is not a solution to}a-1=2a+3\hfill \end{array}\hfill \end{array}$
Verify that -2 is a solution to $3m-2=-4m-\text{16}$ .
When $m=-2$ ,
$\begin{array}{ccccc}& \hfill 3m-2& =& -4m-16\hfill & \\ \hfill \text{becomes}& \hfill 3(-2)-2& =& -4(-2)-16\hfill & \\ & \hfill -6-2& =& 8-16\hfill & \\ & \hfill -8& =& -8\hfill & \begin{array}{c}\text{which is a}\mathit{\text{true}}\text{statement, verifying that}\hfill \\ -2\text{is a solution to}3m-2=-4m-16\hfill \end{array}\end{array}$
Verify that 5 is a solution to $m+6=\text{11}$ .
Substitute 5 into $m+6=\text{11}$ . Thus, 5 is a solution.
Verify that $-5$ is a solution to $2m-4=-\text{14}$ .
Substitute -5 into $2m-4=-\text{14}$ . Thus, -5 is a solution.
Verify that 0 is a solution to $5x+1=1$ .
Substitute 0 into $5x+1=1$ . Thus, 0 is a solution.
Verify that 3 is not a solution to $-3y+1=4y+5$ .
Substitute 3 into $-3y+1=4y+5$ . Thus, 3 is not a solution.
Verify that -1 is a solution to $6m-5+2m=7m-6$ .
Substitute -1 into $6m-5+2m=7m-6$ . Thus, -1 is a solution.
We know that the equal sign of an equation indicates that the number represented by the expression on the left side is the same as the number represented by the expression on the right side.
This number | is the same as | this number |
↓ | ↓ | ↓ |
$x$ | = | 4 |
$x+7$ | = | 11 |
$x-5$ | = | -1 |
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