Solving Distributive Property Equations Worksheet
Understanding the distributive property of multiplication is a crucial skill that you need to have if you are learning to solve algebraic equations.
Whether you’re working with algebraic expressions for the first time or building a stronger foundation in math, mastering this concept will set you up for success in more advanced topics.
In fact, as someone who has studied math well into the post-secondary level, I can say with confidence that understanding how to apply the distributive property is one of the single most important algebraic tools you can have!
That’s why I’ve created a distributive property equations worksheet packed with practice problems that will help you master this skill!
This worksheet is perfect for 8th grade students exploring this concept for the first time, or for more advanced students looking to brush up on their skills.
I’ve made sure to include the worksheet in PDF format, and I’ve also included a full answer key with worked solutions.
But first, let’s take a quick look at how to apply the distributive property with a simple example!
How to Apply the Distributive Property (Simple Example)
At its core, the distributive property of multiplication allows us to “distribute” a term outside a set of parentheses so that it multiplies by each term inside the parentheses.
In general, we can summarize the distributive property as:
\[a(b+c)=ab+ac\]
This shows how the value of \(a\) multiplies by both \(b\) and \(c\).
Let’s take a look at a simple example that shows how this property is applied in practice.
Example: Applying the Distributive Property
Use the distributive property to solve for \(x\) in the equation \(3(x + 4) = 21\).
Step-By-Step Solution
To begin, we distribute the 3 into the brackets, multiplying it by each term.
\[\begin{split} 3(x + 4) &= 21 \\ 3x+12&=21 \end{split} \]
Next, we subtract 12 from both sides of the equation.
\[\begin{split} 3x+12&=21\\ 3x&=9 \end{split} \]
Lastly, we divide both sides of the equation by 3 to solve for the value of the unknown variable.
\[\begin{split} 3x&=9 \\ x&=3\end{split} \]
This method works whether you’re working with positive numbers, negative numbers, or even rational numbers like fractions.
It’s especially important to pay close attention to negative coefficients. In my teaching experience, I have noticed that these types of equations really tend to trip students up. I’ve made sure to include an entire section on the worksheet that focuses on negative coefficients and the distributive property.
Distributing a negative number like -2 requires careful sign management. Remember that when multiplying a negative by a positive the result will be negative. Multiplying a negative by a negative will result in a positive.
For example:
\[\begin{split} &−2(x−5) =&−2x+10 \end{split} \]
Notice how \(-2\) multiplied by \(x\) (a term with a positive coefficient) to produce \(-2x\). By comparison, \(-2\) multiplied by \(-5\) to produce \(10\), a positive number.
Mastering this process will help you become more confident solving equations by working with each side of the equation, no matter how tricky the signs get.
Looking for a more detailed explanation or harder examples? Check out this video I recorded that focuses on applying the distributive property to solve equations!
Distributive Property Equations Worksheet
Below you will find the distributive property worksheet that I put together to help you master this important concept. I have crafted this worksheet to include a wide variety of algebraic expressions.
You will see straightforward linear expressions, as well as more complex expressions involving multiple steps.
The worksheet consists of three parts:
- Part A: Simple Equations (linear equations in one variable)
- Part B: Two-Step Equations with Negative Coefficients (more complex equations with negatives and variables on both sides)
- Part C: Complex Expressions and Linear Equations (two-step equations that combine distribution and inverse operations)
Using This Worksheet and Answer Key
The best part about this solving linear equations worksheet is that it is completely ready to go. You can download it in pdf format and print it to get started right away!
I have made sure to create a set of practice problems that escalates in difficulty as you go. I’ve also made sure to include a full answer key with full worked solutions. This will help make sure that you can check your work while completing the sheet independently with confidence.
Mastering the distributive property of multiplication lays the groundwork for success with more advanced math concepts later on. Use this worksheet for targeted, effective practice.
If you are looking for more helpful worksheets like this one, check out my collection of free printable math worksheets to build confidence and a deeper understanding in algebra!
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