Two Step Equations Worksheets
The first major leap forward for students in prealgebra is working with equations that require multiple steps to solve. When an equation is presented to you, it is balanced meaning that both sides are equal. You can easily rearrange any equation by simply performing the operation of your choice. You just need to make sure to process that operation on both sides of the equal symbol. Whatever you decide to do to one side, will be done to the other. In most cases we are simply trying to get a variable by itself and determine what it is equal to. The most commonly used variable is the letter “x”. These worksheets and lessons help students learn how to manage problems that involve solving equations in at least two steps.
Aligned Standard: 7.EE.B.3
- Solve For X Step-by-Step Lesson- Two thumbs up if you get this one. You get two either way!
- Guided Lesson - Play through on these. Make sure to get rid of the constant first.
- Guided Lesson Explanation - In some cases, I made two steps into three steps.
- Independent Practice - I used all numbers under 20 in the operations to make sure basic operations don't trip you up.
- Matching Worksheet - Find the value of the variables in all cases.
- Practice Worksheet Pack - You will find five practice worksheets here.
- Write the Equation Worksheet Pack - We give you the words. We want the integers in return.
- Two Step Equations in Words Lesson Practice Sheet - This one was written well. I think I'm on version 30 of this.
- Two Step Equations in Words Worksheet - Now you not only need to write the equation, but solve it too.
- Answer Keys - These are for all the unlocked materials above.
Start by getting x by itself. The next step is to take a sentence and turn into a math sentence that is then solvable.
- Homework 1 - In order to get x on the left side we have to remove 4 using addition.
- Homework 2 - Write the sentence as an equation and solve it. Four less than a number divided by 3 is six.
- Homework 3 - For the first step, in order to get x on the left side we have to remove 12 using subtraction.
The sentence based problems really give many students trouble.
- Practice 1 - It is always good to start with numbers that have no variables attached to them.
- Practice 2 - In the second step we will remove the coefficient using division. The opposite of multiplication is division.
- Practice 3 - Write the sentences as equations and solve.
Math Skill Quizzes
Remind students to combine like terms as much as possible and then proceed from there.
- Quiz 1 - Write the sentences as equations and solve. You are basically trying to represent what is presented with numbers and symbols.
- Quiz 2 - Solve for p: 6p + 2p = 72. There are some single steps in here too to allow for some confidence.
- Quiz 3 - You will find you deal a lot with negative values here. Just remember to counter the operations.
How to Approach Two-Step Equations
When you start to learn algebra, it gets more complicated every step of the way. Nonetheless, after learning a single-step equation in which you only have to switch numbers to the other side of the relational operator. For instance, when you have an equation like x + 3 = 0, you need to subtract 3 (since it's the same number on the left-hand-side) on both sides to have an equation x + 3 - 3 = 0 - 3. The answer will be x = -3. However, to solve the two-step equation, we have to learn one more single step. Let's learn it in the form of an example.
For example, we will take the equation 3x + 5 = 65. The entire goal is to get the variable (x) by itself.
The first step, in this case, will be to subtract 5 from both sides of the relational sign (3x + 5 – 5) = (65 – 5).
The result is 3x = 60; however, you haven't found the value of x alone. There is a coefficient attached to x.
In such circumstances, you need to divide with the same number as the coefficient attached to the variable. Therefore, we will divide both sides with 3. 3x / 3 = 60 / 3. So x = 20.
It is all about determining what operations are in play and then just drop the opposites to cancel them out, as you have seen in our example.
The Two Steps You Need to Solve These Problems
These problems can seem much more reasonable when you put them into perspective and think in this manner when tackling them:
1) Start by countering the math operations that are presented to you. Just remember that addition and subtraction will counter one another. Multiplication and division are adversaries as well. Whatever operation you choose to use to create balance, just use the same operation on both sides of the equation and you are all set. This will help you tip the scales in your favor.
2) The last step is just to get the variable by itself. This will again require you to counter the operations that are in place, and you are good to go.