# Pre-Algebra : Two-Step Equations with Fractions

## Example Questions

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### Example Question #1 : Two Step Equations With Fractions

Solve for :

Explanation:

The goal is to isolate the variable on one side.

Subtract  from each side of the equation:

Multiply both sides by :

### Example Question #2 : Two Step Equations With Fractions

Solve for :

Explanation:

The goal is to isolate the variable to one side.

First, convert mixed numbers to improper fractions:

Subtract  from both sides:

Multiply each side by the reciprocal of :

Cross out like terms and multiply:

### Example Question #1 : Two Step Equations With Fractions

Solve for :

Explanation:

Step 1: Add  to both sides:

Step 2: Add to . Remember that when you add fractions, you must find common denominator. The common denominator for and is .   becomes when you multiply both the numerator and the denominator by . Similarly, becomes when you multiply both the numerator and the denominator by .

Step 3: Multiply both sides of the equation by the reciprocal of :

Step 4: Simplify the fraction by dividing the numerator and the denominator by the Greatest Common Factor (GCF). The GCF of and is :

### Example Question #2 : Two Step Equations With Fractions

Solve for :

Explanation:

You are trying to isolate the

To do this you must first subtract both sides by 2 to get

This then becomes a one-step problem where you multiply both sides by 2 to get

### Example Question #3 : Two Step Equations With Fractions

Solve for x:

Explanation:

Once you've isolated x, it's important to find the lowest common denominator so that you can add the two fractions you're working with.

Step 1: Isolate x and convert fractions so that they have a common denominator

Step 2: solve for x

### Example Question #4 : Two Step Equations With Fractions

Solve for .

Explanation:

Cross multiplication is a short-cut that comes from multiplying by the denominators on both sides of an equation. Broken down, it works like this:

The 4's on the left side of the equation cancel out.

Now, do the same with the denominator on the right side.

The 's on the right cancel out.

This is simply the result of removing the denominators, then multiplying them on the opposite sides, i.e. cross multiplication.

Now, to finish solving for , simplify both sides.

Then take the square root to finish.

Solve for :

Explanation:

### Example Question #5 : Two Step Equations With Fractions

Solve for .

Explanation:

First, you want to leave all terms with x on one side and all other terms on the other side. To do this, we can subtract 4/3 from both sides.

We now have

We can now multiply both sides by the reciprocal of 2/5, which is 5/2, to be able to solve for just x.

### Example Question #6 : Two Step Equations With Fractions

Solve for :

Explanation:

Explanation:

The goal is to isolate the variable to one side.

First, convert the mixed numbers to improper fractions:

Subtract from both sides:

Multiply each side by the reciprocal of :

### Example Question #7 : Two Step Equations With Fractions

Solve for ""

Explanation:

1.) Add 8 to both sides, removing the "". It now reads

2.) Multiply both sides by 2, removing the . It now reads

3.) Subtract  from both sides, removing the "". It now reads

4.) Divide both sides by "", resulting in

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