What if you were given an equation like \begin{align*}2x^2  8 = 0\end{align*}
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CK12 Foundation: 0108S Check Solutions to Equations
Guidance
You will often need to check solutions to equations in order to check your work. In a math class, checking that you arrived at the correct solution is very good practice. We check the solution to an equation by replacing the variable in an equation with the value of the solution. A solution should result in a true statement when plugged into the equation.
Example A
Check that the given number is a solution to the equation: \begin{align*}y = 1; \ 3y + 5 = 2y\end{align*}
Solution
Replace the variable in each equation with the given value.
\begin{align*}3(1) + 5 & = 2(1)\\ 3 + 5 & = 2\\ 2 & = 2\end{align*}
This is a true statement. This means that \begin{align*}y = 1\end{align*}
Example B
Check that the given number is a solution to the equation: \begin{align*}z =3; \ z^2 + 2z = 8\end{align*}
Solution:
\begin{align*}3^2 + 2(3) & = 8\\ 9 + 6 & = 8\\ 15 & = 8\end{align*}
This is not a true statement. This means that \begin{align*}z = 3\end{align*}
Let’s use what we have learned about defining variables, writing equations and writing inequalities to solve some realworld problems.
Example C
Tomatoes cost $0.50 each and avocados cost $2.00 each. Anne buys six more tomatoes than avocados. Her total bill is $8. How many tomatoes and how many avocados did Anne buy? Check your answer!
Solution
Define
Let \begin{align*}a = \end{align*}
Translate
Anne buys six more tomatoes than avocados. This means that \begin{align*}a + 6 =\end{align*}
Tomatoes cost $0.50 each and avocados cost $2.00 each. Her total bill is $8. This means that .50 times the number of tomatoes plus 2 times the number of avocados equals 8.
\begin{align*}0.5(a + 6) + 2a &= 8\\ 0.5a + 0.5 \cdot 6 + 2a &= 8\\ 2.5a + 3 &= 8\\ 2.5a &= 5\\ a &= 2\end{align*}
Remember that \begin{align*}a =\end{align*}
Answer
Anne bought 2 avocados and 8 tomatoes.
Check
If Anne bought two avocados and eight tomatoes, the total cost is: \begin{align*}(2 \times 2) + (8 \times 0.5) = 4 + 4 = 8\end{align*}
Watch this video for help with the Examples above.
CK12 Foundation: Check Solutions to Equations
Vocabulary
 A solution an equation should result in a true statement when plugged into the equation.
Guided Practice
Check that the given number is a solution to the equation: \begin{align*}x = \frac{1}{2}; \ 3x + 1 = x\end{align*}
Solution:
\begin{align*} 3 \left (  \frac{1}{2} \right ) + 1 & =  \frac{1}{2}\\ \left (  \frac{3}{2} \right ) + 1 & =  \frac{1}{2}\\  \frac{1}{2} & =  \frac{1}{2}\end{align*}
This is a true statement. This means that \begin{align*}x =  \frac{1}{2}\end{align*}
Practice
For 19, check whether the given number is a solution to the corresponding equation.

\begin{align*}a = 3; \ 4a + 3 = 9\end{align*}
a=−3; 4a+3=−9 
\begin{align*}x = \frac{4}{3}; \ \frac{3}{4}x + \frac{1}{2} = \frac{3}{2}\end{align*}
x=43; 34x+12=32 
\begin{align*}y = 2; \ 2.5y  10.0 = 5.0\end{align*}
y=2; 2.5y−10.0=−5.0 
\begin{align*}z = 5; \ 2(5  2z) = 20  2(z  1)\end{align*}
z=−5; 2(5−2z)=20−2(z−1)  \begin{align*}a = 10; \ 5a7=43\end{align*}
 \begin{align*}x = \frac{2}{3}; 3x+5=7 \end{align*}
 \begin{align*}y = 9; \ \frac{x}{3}\cdot 10 = 30\end{align*}
 \begin{align*}z = \frac{1}{2}; \ 2z=1.5z\end{align*}
 \begin{align*}z = 0.5; \ z(1  2z) = 6 + 6(4z  3)\end{align*}
 The cost of a Ford Focus is 27% of the price of a Lexus GS 450h. If the price of the Ford is $15000, what is the price of the Lexus?