Solving two-step equations with fractions can seem a bit intimidating at first, but with the right approach and understanding, you’ll quickly master the process. In this guide, we’ll walk you through the process of solving two-step equations involving fractions, step by step. Let’s get started!
Step 1: Understand the Problem
Before diving into solving the equation, it’s essential to understand what a two-step equation with fractions is. A two-step equation is an algebraic equation that requires two operations (addition, subtraction, multiplication, or division) to isolate the variable. In our case, the equation will also involve fractions.
An example of a two-step equation with fractions is:
(1/2)x + 3 = 7
Step 2: Eliminate the Fractions (Optional)
For some, working with fractions can be challenging. If you’re more comfortable working with whole numbers, you can eliminate the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators. This step is optional, as you can still solve the equation with fractions if you prefer.
For our example equation, the LCM of the denominator 2 is simply 2. So, we’ll multiply both sides of the equation by 2:
(2)(1/2)x + (2)3 = (2)7
This simplifies to:
x + 6 = 14
Step 3: Perform the First Operation
Now that we’ve eliminated the fractions (or chosen to keep them), it’s time to perform the first operation to isolate the variable. In this case, we’ll subtract 6 from both sides of the equation:
x + 6 - 6 = 14 - 6
This simplifies to:
x = 8
Step 4: Check Your Answer
It’s always a good idea to check your answer by substituting the value you found for the variable back into the original equation. If the equation holds true, you’ve found the correct solution.
For our example, let’s plug x = 8 back into the original equation:
(1/2)x + 3 = 7 (1/2)(8) + 3 = 7 4 + 3 = 7 7 = 7
Since the equation holds true, our solution is correct: x = 8.
Key Takeaways for Solving Two-Step Equations with Fractions
- Understand the problem and identify the two-step equation with fractions.
- Optionally, eliminate the fractions by multiplying both sides of the equation by the LCM of the denominators.
- Perform the first operation to isolate the variable.
- Check your answer by substituting the value back into the original equation.
By following these easy-to-understand steps, you’ll be able to confidently solve two-step equations with fractions. With constant practice, solving equations like this will become a thing of the past.