Solve equations involving like terms

Key Notes:

What are Like Terms?

• Like terms are terms that have the same variable(s) raised to the same power.
• Only the coefficients (numbers in front) can be different.

✅ Examples of like terms:

• 3x and −5x
• 2y² and 7y²
• 4a and a (remember a=1a)

❌ Not like terms:

• 2x and 2y (different variables)
• x and x² (different exponents)

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Steps to Solve Equations with Like Terms

Step 1: Identify and combine like terms on each side of the equation.

Step 2: Use properties of equality (addition/subtraction) to isolate the variable term.

Step 3: Use multiplication/division to solve for the variable.

Step 4: Check your solution by substituting it back into the original equation.

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Example 1:

3x+5x−4=12

Step 1: Combine like terms on the left: 8x−4=12

Step 2: Add 4 to both sides: 8x=16

Step 3: Divide both sides by 8: x=2

Step 4: Check: 3(2)+5(2)−4=6+10−4=12✔

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Example 2:

7y−3+2y=14

Step 1: Combine like terms: 9y−3=14

Step 2: Add 3 to both sides: 9y=17

Step 3: Divide by 9: y=17/9

Step 4: Check: Substitute y=17/9​ into the original equation.

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Common Mistakes to Avoid

• ❌ Forgetting to combine like terms first.
• ❌ Combining terms that are not alike.
• ❌ Making sign mistakes with negative numbers.

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Practice Problems

• 4x+7x=33
• 5y−2y+8=17
• 3a+6−a=14
• 8m−2+5m+1=29
• 10x+2x−5=43

Like terms are terms that have the same variables raised to the same powers. To subtract like terms, subtract their coefficients.

Learn with an example

let’s practice!