Solving Multistep Equations Made Easy

Solving Multistep Equations: A Step-by-Step Guide

Solving multistep equations can be a daunting task for many students. These equations require a series of operations to be performed in a specific order, and it’s easy to get lost in the process. However, with a clear understanding of the steps involved and some practice, solving multistep equations can become a breeze.

Understanding the Basics

Before we dive into solving multistep equations, let’s quickly review the order of operations. The order of operations is a set of rules that dictates the order in which operations should be performed when there are multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations:

• Parentheses: Evaluate expressions inside parentheses first.
• Exponents: Evaluate any exponential expressions next.
• Multiplication and Division: Evaluate any multiplication and division operations from left to right.
• Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Step 1: Identify the Problem

When solving multistep equations, it’s essential to identify the problem first. Read the equation carefully and identify the variables, constants, and operations involved. Take note of any parentheses, exponents, or other grouping symbols that may affect the order of operations.

Step 2: Follow the Order of Operations

Once you’ve identified the problem, follow the order of operations to simplify the equation. Start by evaluating any expressions inside parentheses, then move on to exponents, multiplication and division, and finally addition and subtraction.

Step 3: Combine Like Terms

As you simplify the equation, combine like terms to make the equation more manageable. Like terms are terms that have the same variable raised to the same power. For example, 2x and 3x are like terms, while 2x and 3y are not.

Step 4: Isolate the Variable

The final step is to isolate the variable. This means getting the variable by itself on one side of the equation. To do this, you may need to add, subtract, multiply, or divide both sides of the equation by the same value.

📝 Note: When isolating the variable, be careful not to change the equation's meaning. Make sure to perform the same operation on both sides of the equation.

Example Problem

Let’s try solving a multistep equation together. Suppose we have the equation:

2(x + 3) = 12

Step 1: Identify the Problem

The equation is 2(x + 3) = 12. We have a variable x, a constant 3, and the operations multiplication and addition.

Step 2: Follow the Order of Operations

First, we need to evaluate the expression inside the parentheses. To do this, we need to distribute the 2 to the terms inside the parentheses.

2x + 6 = 12

Step 3: Combine Like Terms

We don’t have any like terms in this equation, so we can move on to the next step.

Step 4: Isolate the Variable

To isolate the variable x, we need to get rid of the constant term 6. We can do this by subtracting 6 from both sides of the equation.

2x = 12 - 6 2x = 6

Next, we need to get rid of the coefficient 2. We can do this by dividing both sides of the equation by 2.

x = 6 ÷ 2 x = 3

And that’s it! We’ve solved the multistep equation.

Tips and Tricks

Solving multistep equations requires practice, patience, and attention to detail. Here are some tips and tricks to help you improve your skills:

• Read the equation carefully: Take your time to read the equation carefully and identify the variables, constants, and operations involved.
• Use parentheses: Use parentheses to group terms and operations together. This can help you follow the order of operations more easily.
• Check your work: Always check your work to ensure that you’ve solved the equation correctly.
• Practice, practice, practice: The more you practice solving multistep equations, the more confident you’ll become.

Conclusion

Solving multistep equations is a skill that requires practice, patience, and attention to detail. By following the order of operations, combining like terms, and isolating the variable, you can solve even the most complex multistep equations. Remember to read the equation carefully, use parentheses, check your work, and practice regularly to improve your skills.

Related Terms:

• Solving Multi Step Equations Worksheet