Determining Whether a Decimal is a Solution of an Equation

Determining Whether a Decimal is a Solution of an Equation

Solving equations with decimals is important in our everyday lives because money is usually written with decimals. When applications involve money, such as shopping for yourself, making your family’s budget, or planning for the future of your business, you’ll be solving equations with decimals.

Now that we’ve worked with decimals, we are ready to find solutions to equations involving decimals. 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, an integer, a fraction, or a decimal. We’ll list these steps here again for easy reference.

Example

Determine whether each of the following is a solution of \(x-0.7=1.5\text{:}\)

1. \(\phantom{\rule{0.2em}{0ex}}x=1\)
2. \(\phantom{\rule{0.2em}{0ex}}x=-0.8\)
3. \(\phantom{\rule{0.2em}{0ex}}x=2.2\)

Solution

Subtract.

Since \(x=1\) does not result in a true equation, \(1\) is not a solution to the equation.

Subtract.

Since \(x=-0.8\) does not result in a true equation, \(-0.8\) is not a solution to the equation.

Subtract.

Since \(x=2.2\) results in a true equation, \(2.2\) is a solution to the equation.

Optional Video: Solving One Step Equations Involving Decimals