How To Solve Equations With Variables On One Side

Table Of Contents

Key concepts of Solving Equations With Variables:
Different forms for solving equations with variables:
How do you teach solving equations in different forms?

Step 1: Ignore (or cover) the side of the equation that is not being simplified
Step 2: Distribute (if needed) for the side being simplified
Step 3: Combine like terms (if needed) for the side being simplified
Step 4: Use inverse operations to solve the equation

Examples:

Distributive Property
Combine Like Terms
Distribute & Combine Like Terms

Why teach solving equations in different forms this way?
Vocabulary for teaching solving equations in different forms:
Misconceptions and errors students are likely to have:
Frequently Asked Questions On Solving Equations With Variables On One Side:

How do you solve equations with Distributive Property?
How do you solve equations by combining like terms?
How do I solve an equation that includes combining like terms and the Distributive Property?
Do you combine like terms first or distribute?

Key concepts of Solving Equations With Variables:

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Students have solved one-step and two-step equations; however, they do not have experience with multi-step equations. Students often forget that equations are just two equal expressions. When the equation requires students to combine like terms or distribute before solving one side, they may get overwhelmed. This is an essential skill because equations will continue to get more complex in later grade levels.

Different forms for solving equations with variables:

One- and two-step equations are commonly solved by students. Multi-step equations where the variable is on one side can require students to use the Distributive Property and combine like terms. Here are some examples of the different forms:

Combine like terms and solve
- Example: 4x – 2x + 5 = -7
- Example: -4x – 12 + 2 = 6
Distribute and solve
- Example: -2(4x – 3) = -10
Distribute, combine like terms, and solve
- Example: ½ (-6x + 4) – 8 = -12

How do you teach solving equations in different forms?

Step 1: Ignore (or cover) the side of the equation that is not being simplified

Tell students to focus on the side of the equation that needs to be simplified, and treat it as its own expression.

Step 2: Distribute (if needed) for the side being simplified

Remind students that if there is a value outside of parentheses, multiply it to everything inside of the parentheses.

SPECIAL CASE: When there is only distributing and the constant on the right side can be divided by the constant in front of the parentheses evenly, students divide instead of distributing. This can simplify solving when the result is still a whole number on the right side.

Step 3: Combine like terms (if needed) for the side being simplified

Remind students how to combine like terms if needed. Students should be careful of their signs!

Step 4: Use inverse operations to solve the equation

Remind students of the inverse operations, as well as which order they should perform the operations.

Examples:

Distributive Property

Combine Like Terms

Distribute & Combine Like Terms

Why teach solving equations in different forms this way?

Having students focus on each side of the equation as its own expression can help them use their prior knowledge to help solve the equation.
Teaching students to eliminate the parentheses first by distributing helps get rid of the extra symbols.

Vocabulary for teaching solving equations in different forms:

Coefficient: A number that multiplies a variable. If there is no coefficient in front of a variable, the coefficient is 1.

Variable: A symbol (usually a letter) that is used to represent a number in an expression or equation.

Like terms: Terms that have the same variables, raised to the same power.

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Constants are like terms.

Distribute: When a factor is multiplied by terms within parentheses, it is the same as multiplying the factor by each of the terms separately.

Misconceptions and errors students are likely to have:

Computational errors with operations involving negative values:
- You can remind students that the sign in front of values (+ or -) will tell them if a number is positive or negative.
- You may also need to remind them of the rules for operations with negative numbers.

Combining terms that are not like terms:
- Remind students that terms can only be combined if the terms have the same variable (or are constants).

Not distributing correctly (incorrect signs, not all terms are multiplied):
- Students may need to be reminded of the rules for multiplying with negative numbers.
- You may encourage students to draw the arrows showing what values are distributed.
- Color coding can help struggling students.

Incorrectly using inverse operations to solve the equation:
- Have students identify what needs to be moved to the other side of the equation first, and then what operation is needed to move it.
- For these equation forms, students should only need to use two steps to solve the problem.

Also read: 5 Steps To Teach The Product Rule Of Exponents

Frequently Asked Questions On Solving Equations With Variables On One Side:

How do you solve equations with Distributive Property?

You can divide both sides by what is in front of the parentheses, although check first to see if the constant is divisible by that number.

You can also distribute the constant in front of the parentheses and multiply it with everything inside of the parentheses. Then solve the equation using inverse operations.