Solving Equations By Combining Like Terms

In this lesson, we will look into solving equations by combining like terms.

What are Like Terms?
Like terms are terms that contain the same variable with the same exponent. Constant terms are like terms because they do not have any variables.

Here are some examples of like terms:

• 2x and 5x are like terms because both contain the same variable.
• 6 and 10 are like terms because both are constant terms.
• 2y² and 7y² are like terms because both contain the same variable with the same exponent.

Some examples of terms that are not like terms are:

• 4x and 4y are not like terms because the variables are different.
• 5z and 11 are not like terms because one term has a variable and the other is constant.
• 3x² and 3x are not like terms because the variables are the same, but the exponents are different.

Two terms that are like terms may be combined into one term by adding or subtracting.
Very often, we would need to combine like terms when solving equations.

How to solve equations by combining like terms?
Example:

Solve 6x – 4x – 3 = 11

Solution:

6x – 4x – 3 = 11
2x– 3 = 11 (combine like terms)
2x – 3 + 3 = 11 + 3 (add 3 to both sides)
2x = 14 (divide 2 on both sides)
x = 7

Check:

6x – 4x – 3 = 11
(6 • 7) – (4 • 7) – 3 = 11 (substitute x = 7 into the original equation)

Example:

Solve x + 2x – 7 = 5

Solution:

x + 2x – 7 = 5
3x – 7 = 5 (combine like terms)
3x – 7 + 7 = 5 + 7 (add 7 to both sides)
3x = 12 (Divide both sides by 3)
x = 4

Check:

x + 2x – 7 = 5
4 + 8 – 7 = 5 (substitute x = 4 into the original equation)

Combining Like Terms
Explain the concept of “like terms” and show how polynomials can be simplified by combining like terms.

Solving an Equation that Requires Combining Like Terms

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