### 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 .

**Answer**

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.

- 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?

### Review (Answers)

To view the Review answers, open this PDF file and look for section 1.8.