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Mathematics » Mathematics 103: Integers » Solve Equations Using Integers; The Division Property of Equality

# Determining Whether a Number is a Solution of an Equation

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## Determining Whether a Number is a Solution of an Equation

In Mathematics 102, we saw that a solution of an equation is a value of a variable that makes a true statement when substituted into that equation. In that section, we found solutions that were whole numbers. Now that we’ve worked with integers, we’ll find integer solutions to equations.

The steps we take to determine whether a number is a solution to an equation are the same whether the solution is a whole number or an integer.

### How to Determine Whether a Number is a Solution to an Equation

1. Substitute the number for the variable in the equation.
2. Simplify the expressions on both sides of the equation.
3. Determine whether the resulting equation is true.
• If it is true, the number is a solution.
• If it is not true, the number is not a solution.

## Example

Determine whether each of the following is a solution of $$2x-5=-13\text{:}$$

1. $$\phantom{\rule{0.2em}{0ex}}x=4\phantom{\rule{0.6em}{0ex}}$$
2. $$\phantom{\rule{0.2em}{0ex}}x=-4\phantom{\rule{0.6em}{0ex}}$$
3. $$\phantom{\rule{0.2em}{0ex}}x=-9.$$

### Solution

 Substitute 4 for x in the equation to determine if it is true. Multiply. Subtract.

Since $$x=4$$ does not result in a true equation, $$4$$ is not a solution to the equation.

 Substitute −4 for x in the equation to determine if it is true. Multiply. Subtract.

Since $$x=-4$$ results in a true equation, $$-4$$ is a solution to the equation.

 Substitute −9 for x in the equation to determine if it is true. Substitute −9 for x. Multiply. Subtract.

Since $$x=-9$$ does not result in a true equation, $$-9$$ is not a solution to the equation.