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# Solving Two-Step Linear Equations with Fractions

A linear equation is an equation in which the variable(s) are multiplied by or added to numbers with nothing more complicated than that. Linear equations don't contain square roots, exponents, $\frac{1}{x}$ , or other more complex components like that.

The solution for an equation is the number that can be plugged in for the variable to make a true math statement. For example, in the above statement $4x+9=21$ , if you plug 3 in for the x, you get $4×3+9=21$ , which is a true statement. $4×3=12$ , $12+9=21$ . Sometimes linear equations can have more than one correct solution.

One-step linear equations are generally in the form of $x+y=z$ or $x×y=z$ . Two-step linear equations are in the form of something like $ax+y=z$ . In this tutorial, we're looking at two-step equations that have fractions in them.

## Solving two-step linear equations

To solve a two-step linear equation, we need to use inverse operations to undo each operation in the equation in reverse PEMDAS order.

Example 1

Solve $5x+8=28$ .

Because we're going in reverse order, we are going to undo the addition first. So we subtract 8 from each side of the equation.

$5x+8-8=28-8$

Simplify by performing the subtraction.

$5x=20$

Next, we are going to undo the multiplication by using division. We will divide each side of the equation by 5, which will isolate x.

$\frac{5x}{5}=\frac{20}{5}$

Simplify by performing the division.

$x=4$

Finally, we check our answer by seeing if it works in the original equation.

$\left(5×4\right)+8=28$

$20+8=28$

It works, so we have found the solution for the variable x in the two-step linear equation.

## Two-step linear equations with fractions

Solving a two-step linear equation with fractions involves undoing division instead of undoing multiplication. We still undo each operation in reverse order. Let's look at an example to see how to do this.

Example 2

$\frac{x}{5}-10=3$

Our first step is to undo the subtraction, so we will add 10 to each side.

$\frac{x}{5}-10+10=3+10$

$\frac{x}{5}=13$

Next, we undo the division by multiplying each side of the equation by 5.

$\frac{x}{5}×5=13×5$

Simplify by performing the multiplication.

$x=65$

Now let's check to see if our solution works in the original equation.

$\frac{65}{5}-10=3$

$13-10=3$

$3=3$

It does work, so we have found the correct solution. And that is how we work two-step linear equations with fractions.

## Flashcards covering the Solving Two-Step Linear Equations with Fractions

Algebra 1 Flashcards