section 1.6 Learning Objectives
1.6: Solving Equations Containing Decimals
- Solve one-step equations containing decimals
- Solve multi-step equations containing decimals
think about it
Can you determine what you would do differently if you were asked to solve equations like these?
Solve [latex]{12.5}+{ t }= {-7.5}[/latex].
What makes this example different than the previous ones? Use the box below to write down a few thoughts about how you would solve this equation with decimals.
Solve one-step equations containing decimals
In the following video, two examples of using the addition property of equality with decimal numbers are shown.
Solve multi-step equations containing decimals
Sometimes, you will encounter a multi-step equation with decimals. If you prefer not working with decimals, you can use the multiplication property of equality to multiply both sides of the equation by a a factor of 10 that will help clear the decimals. See the example below.
Example 1
Solve [latex]3y+10.5=6.5+2.5y[/latex] by clearing the decimals in the equation first.
In the following example, you will see the same problem as the last example, but solved without clearing the decimals. It might be helpful to compare the two methods and decide which method you prefer.
Example 2
Solve [latex]3y+10.5=6.5+2.5y[/latex] without clearing decimals
In the following video, we show another example of clearing decimals first to solve a multi-step linear equation.
Here is a reminder of the steps to follow when you solve multi-step equations.
Solving Multi-Step Equations
1. Simplify each side by clearing parentheses and combining like terms.
2. (Optional) Multiply to clear any fractions or decimals.
3. Add or subtract to isolate the variable term—you may have to move a term with the variable.
4. Multiply or divide to isolate the variable.
5. Check the solution.
We conclude with an example that requires step 1 – clearing parentheses through distribution.
Example 3
Solve: [latex]0.7(x+1.02)+0.2x=0.5(x-1.2)-6.24[/latex]