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# Checking Solutions to Equations

## Substitute values for variables to check equation solutions

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Checking Solutions to Equations

### Checking Solutions: Equations

You will often need to check solutions to equations in order to check your work. In a math class, verifying that you arrived at the correct solution is very good practice. We check a solution to an equation by replacing the variable in the equation with the value of the solution. A solution should result in a true statement when simplified.

#### Checking Solutions to Equations

1. Check that the given number is a solution to the equation:

Replace the variable  in the equation with the given value, -1.

2 = 2 is a true statement. This means that is a solution to .

2. Check that the given number is a solution to the equation:

Replace the variable  in the equation with the given value, 3.

15 = 8 is not a true statement. This means that is not a solution to .

Let’s use what we have learned about defining variables, writing equations and writing inequalities to solve some real-world problems.

#### Real-World Applications

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! Define Let equal the number of avocados Anne buys. Translate Anne buys six more tomatoes than avocados. This means that is equal to the number of tomatoes. 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.

Remember that  represents the number of avocados. Since , Anne buys two avocados. The number of tomatoes is .

Anne bought 2 avocados and 8 tomatoes.

Check

If Anne bought two avocados and eight tomatoes, the total cost would be: . The answer checks out.

### Example

#### Example 1

Check that the given number is a solution to the equation:

is a true statement. This means that is a solution to .

### Review

For 1-9, check whether the given number is a solution to the corresponding equation.

1. 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?

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### Vocabulary Language: English

Equation

An equation is a mathematical sentence that describes two equal quantities. Equations contain equals signs.

inequality

An inequality is a mathematical statement that relates expressions that are not necessarily equal by using an inequality symbol. The inequality symbols are $<$, $>$, $\le$, $\ge$ and $\ne$.

solution

A solution to an equation or inequality should result in a true statement when substituted for the variable in the equation or inequality.