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# Decimals in Linear Equations Help

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## Solving Equations with Decimals

Because decimal numbers are fractions in disguise, the same trick can be used to “clear the decimal” in equations with decimal numbers. Count the largest number of digits behind each decimal point and multiply both sides of the equation by 10 raised to the power of that number.

#### Examples

0.25 x + 0.6 = 0.1

Because there are two digits behind the decimal in 0.25, we need to multiply both sides of the equation by 10 2 = 100. Remember to distribute the 100 inside the parentheses.

### Decimals in Linear Equations Practice Problems

#### Practice

Solve for x after clearing the decimal. If your solution is a fraction, convert the fraction to a decimal.

1. 0.3( x – 2)+ 0.1 = 0.4

2. 0.12 – 0.4( x + 1)+ x = 0.5 x + 2

3. 0.015 x – 0.01 = 0.025 x + 0.2

4. 0.24(2 x – 3)+ 0.08 = 0.6( x + 8) – 1

5. 0.01(2 x + 3) – 0.003 = 0.11 x

#### Solutions

Practice problems for these concepts can be found at: Algebra Linear Equations Practice Test.

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