# Solving Linear Equations

## Solve Equations with Fraction or Decimal Coefficients


### Solve Equations with Fraction Coefficients

Let’s use the General Strategy for Solving Linear Equations introduced earlier to solve the equation 
This method worked fine, but many students don’t feel very confident when they see all those fractions. So we are going to show an alternate method to solve equations with fractions. This alternate method eliminates the fractions.
We will apply the Multiplication Property of Equality and multiply both sides of an equation by the least common denominator of all the fractions in the equation. The result of this operation will be a new equation, equivalent to the first, but with no fractions. This process is called clearing the equation of fractions. Let’s solve the same equation again, but this time use the method that clears the fractions.
Notice in  that once we cleared the equation of fractions, the equation was like those we solved earlier in this chapter. We changed the problem to one we already knew how to solve! We then used the General Strategy for Solving Linear Equations.
In the next example, we’ll have variables and fractions on both sides of the equation.
In , we’ll start by using the Distributive Property. This step will clear the fractions right away!
Many times, there will still be fractions, even after distributing.

### Solve Equations with Decimal Coefficients

Some equations have decimals in them. This kind of equation will occur when we solve problems dealing with money and percent. But decimals are really another way to represent fractions. For example,  and  So, when we have an equation with decimals, we can use the same process we used to clear fractions—multiply both sides of the equation by the least common denominator.
The next example uses an equation that is typical of the ones we will see in the money applications in the next chapter. Notice that we will distribute the decimal first before we clear all decimals in the equation.

### Key Concepts

1. Solve equations with fraction coefficients by clearing the fractions.

### Section Exercises


### Practice Makes Perfect

Solve equations with fraction coefficients 
In the following exercises, solve the equation by clearing the fractions.
Solve Equations with Decimal Coefficients 
In the following exercises, solve the equation by clearing the decimals.

### Everyday Math


### Writing Exercises


### Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ Overall, after looking at the checklist, do you think you are well-prepared for the next Chapter? Why or why not?



### Chapter Review Exercises


### Solve Equations using the Subtraction and Addition Properties of Equality

In the following exercises, determine whether the given number is a solution to the equation.
In the following exercises, solve the equation using the Subtraction Property of Equality.
In the following exercises, solve the equation using the Addition Property of Equality.
In the following exercises, solve the equation.
In the following exercises, translate each English sentence into an algebraic equation and then solve it.
In the following exercises, translate into an algebraic equation and solve.

### Solve Equations using the Division and Multiplication Properties of Equality

In the following exercises, solve each equation using the Division Property of Equality.
In the following exercises, solve each equation using the Multiplication Property of Equality.
In the following exercises, solve each equation.

### Solve Equations with Variables and Constants on Both Sides

In the following exercises, solve the equations with constants on both sides.
In the following exercises, solve the equations with variables on both sides.
In the following exercises, solve the equations with constants and variables on both sides.
In the following exercises, solve each linear equation using the general strategy.

### Solve Equations with Fraction or Decimal Coefficients

In the following exercises, solve each equation by clearing the fractions.
In the following exercises, solve each equation by clearing the decimals.

### Chapter Practice Test

In the following exercises, solve each equation.