Solve Two-Step Equations

Before Lesson

In this lesson, students learn to solve two-step equations. Have students show readiness by applying order of operations to simplify expressions with integers. For example: 18+6 ÷ 6, -4x-2+4, -9-5+3.

Background

Explain to students that two-step equations involve two different operations, such as multiplication and addition. Ask students why it’s helpful to take time before beginning the solution process to decide which different operations they must apply to solve an equation.

Guided Practice

• Translate Verbal Sentences into Two-Step Equations
• Solve Two-Step Equations

Core Skill

Make Sense of Problems: Allow students time to read the sidebar. Then have them complete the activity at the bottom by making a deliberate mistake when solving Example 4. Tell students that dropping negative signs is an extremely common mistake. Explain that this is something to check for if they got the wrong answer, and if they find they make it repeatedly, it can help to circle the number and the negative sign throughout the solution process to make sure it is not dropped.

Evaluate Expressions: Remind students that they can use inverse operations in the opposite order of operations to solve an equation. The first inverse operation would be to subtract 4 to get the equation 5x=20. Then divide by 5 to determine that x=4.

Extension

Fill in the Blanks: Write the following Cloze passage and word choices on the board. Have students fill in the blanks. Tell them that a word can be used more than once (answer, inverse, isolate, operation, two-step).

In order to solve ___ equations, I must ___ the variable. This involves using operations to undo the ___ on one side. I must perform the correct __, otherwise I will get the wrong ____.

Use Concepts to Solve Challenging Problems: Give students equations with three or more steps, such as 4+x/5-2=2. Have them solve the problems and describe how the order of operations helped them know which operations to do in which order.