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Simplifying Linear Expressions Worksheets

Linear expressions are algebraic statements that contain terms that consist of constants and variables. Unlike equations, expressions do not contain an equal sign. As the word "linear" indicates, they can be used to draw lines that help us make predictions and decisions. They are fundamental tools in science. Scientists will often create linear expression to help them describe or explore the relationship and nature of two distinct variables. Once they define an accurate expression it can be used to calculate rates, position, and determine trends. This allows for accurate and reliable predictions of what will occur in other conditions with these two variables. On these worksheets and lessons we will learn how to reduce and rearrange these expressions to make them work better for us and male the math more understandable and workable.

Aligned Standard: Grade 7 Expression & Equations - 7.EE.A.1

  • Answer Keys - These are for all the unlocked materials above.

Homework Sheets

When you throw just a smudge of geometry in there with expressions students tend to draw a blank.

  • Homework 1 - A rectangle is eight times as long as its width. One way to write an expression to find the perimeter would be: m + m + 8m + 8m
  • Homework 2 - Aliya says the two expressions 6(a + 3) + 3a and 3(3a + 6) are equivalent? Is she correct? Explain why or why not?
  • Homework 3 - An equilateral triangle has a perimeter of (6x + 12). What is the length of each side of the triangle?

Practice Worksheets

It's all about combining those like terms in the expressions.

  • Practice 1 - Write an equivalent expression for 8(2x + 10) - 12
  • Practice 2 - See if you can break this down.
  • Practice 3 - An equilateral triangle has a perimeter of (81x + 63). What is the length of each side of the triangle?

Math Skill Quizzes

Don't let the exponents confuse you, they are just a type of variable like anything else.

  • Quiz 1 - Evaluate: (5x - 2y) X 2 - (8 - xy + 8) for x = -3 and y = 5
  • Quiz 2 - Simplify all the expressions.
  • Quiz 3 - Evaluate:6x - 8y + 6x - 4xy + 6 for x = -2 and y = 4.

How Do You Simplify Linear Expressions?

Simplifying linear expressions is a commonly occurring mathematical operation for any student that is working with algebra. Learning this technique can greatly help you understand how to bend expressions and even equations to your will and solve them or simply make them easier to work with. Many students are often confused in terms of what is the right way of simplifying a linear expression.

There is a strategy that you can use to break down most linear expression to their simplest form. It starts will focusing your energy on any brackets or parentheses that exist. Your next step is to solve any exponents that may be present. From there you should look for any like terms and combine them. If there are multiple constants, put all of those together.

So, let's learn to simplify some linear expressions with the help of a few examples:

-2 (v + 3) + 6v

The rule that needs to be used here is called BODMAS i.e. (Bracket, divide, multiply, addition, and subtraction). This is the order in which the equation needs to be solved.

Let's apply this rule on the equation step by step: -2v + 6 + 6v

Now, it's time to add the values that have the same variables. In this case we can combine the like terms and the coefficients that are attached to them (-2v and 6v). We are left with the following: 4v + 6. We could reduce it further because 2 divides into both terms, we would be left with: 2v + 3.

Let's try another example problem: 5 (4y + 2) - 12

Using the same rule, get rid of the bracket and we have: 20y + 10 - 12

We then do some simple subtraction of the constants (10-12): 20y - 2

In this case, the equation can be simplified even further because the two constants can be divided by the same number, 2. Hence the final expression becomes: 2(10y - 1).

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