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Two Step Equations

Answer Keys Here

Aligned To Common Core Standard:

Grade 7 Expressions & Equations - 7.EE.B.3

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 Now, firstly we will subtract 5 from both sides of the relational sign, i.e., 3x + 5 - 5 = 65 - 5. The resultant 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 | x = 20. These worksheets and lessons help students learn how to manage problems that involve solving equations in at least two steps.

Printable Worksheets And Lessons

Homework Sheets

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.

Practice Worksheets

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.

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. What ever operation you choose to use to create balance, just use the same operation on both sides of the equation and you are all set. 2) The last step is just to get the variable by itself. This will again ask you to counter the operations that are in place and you are good to go.