Linear Expression Operations

Grade 7 · algebra · 66 practice problems · read aloud

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What Are Linear Expression Operations? 🤔

Linear expressions are math phrases with variables (like x), numbers, and operations, but no exponents higher than 1. We work with them by adding, subtracting, and combining like terms. This helps us simplify problems and solve real-world situations!

How to Work With Linear Expressions

  1. Identify like terms - terms with the same variable and exponent
  2. Combine coefficients - add or subtract the numbers in front
  3. Keep variables unchanged - the variable part stays the same
  4. Simplify constants - combine regular numbers without variables

Worked Examples ✨

Example 1: Adding Expressions

Problem: (3x + 5) + (2x - 2)

Step 1: Group like terms → (3x + 2x) + (5 - 2)

Step 2: Combine coefficients → 5x + 3

Answer: 5x + 3

Example 2: Subtracting Expressions

Problem: (4y + 7) - (2y + 3)

Step 1: Distribute the negative → 4y + 7 - 2y - 3

Step 2: Combine like terms → (4y - 2y) + (7 - 3)

Step 3: Simplify → 2y + 4

Common Mistakes to Avoid 🚫

  • Forgetting to distribute negatives: When subtracting, remember to change ALL signs in the second expression
  • Combining unlike terms: 3x + 2y cannot be combined - they're different variables!
  • Dropping constants: Don't forget about the plain numbers without variables

Tips & Tricks 💡

  • Use highlighters to color-code like terms
  • Remember the "like term checklist": same variable, same exponent
  • Draw arrows to match up terms before combining
  • Always double-check your signs!

Practice Makes Perfect! 📚

Try these practice ideas:

  • Create your own expression cards and match like terms
  • Solve 2-3 problems daily to build confidence
  • Check your work by substituting a number for the variable
  • Practice with: (5x + 3) + (2x - 1) and (7y - 4) - (3y + 2)

Practice problems

6 of the 66, worked through step by step — try them before opening the answer.

1 (3x + 7) - (2x - 5) = ?

Hint: Remember to distribute the negative sign to all terms in the second expression before combining like terms.

Show the answer

Answer: x + 12

  1. Distribute the negative sign** The minus sign in front of (2x - 5) means we subtract both terms inside the parentheses: = 3x + 7 - 2x - (-5) = 3x + 7 - 2x + 5 **
  2. Combine like terms** First, combine the x terms: 3x - 2x = 1x (or just x) Then, combine the constants: 7 + 5 = 12 **
  3. Write the final expression** x + 12 **Final Answer:** x + 12

Let's solve step by step. We start with: (3x + 7) - (2x - 5) **

2 (3x + 7) + (2x - 5) = ?

Hint: Combine like terms by adding coefficients of the same variables and constant terms separately.

Show the answer

Answer: 5x + 2

  1. Remove the parentheses** Since we are adding the two expressions, the parentheses do not change the signs: 3x + 7 + 2x - 5 --- **
  2. Group like terms** Like terms are terms with the same variable part and constant terms. - Terms with x: 3x and 2x - Constant terms: 7 and -5 So we rewrite: (3x + 2x) + (7 - 5) --- **
  3. Combine like terms** 3x + 2x = 5x 7 - 5 = 2 So we have: 5x + 2 --- **
  4. Write the final answer** The simplified expression is: 5x + 2

Let's solve the problem step by step. We are given: (3x + 7) + (2x - 5) --- **

3 (3x + 7) + (5x - 4) = ?

Hint: Combine like terms by adding coefficients of the same variable and constant terms separately.

Show the answer

Answer: 8x + 3

  1. Remove the parentheses** Since there is only addition between the parentheses, we can remove them without changing the signs: 3x + 7 + 5x - 4 **
  2. Identify like terms** Like terms are terms with the same variable part: - Terms with x: 3x and 5x - Constant terms: 7 and -4 **
  3. Combine the like terms** First, combine the x terms: 3x + 5x = 8x Next, combine the constant terms: 7 - 4 = 3 **
  4. Write the final expression** Putting them together: 8x + 3 **Final Answer:** 8x + 3

Let's solve the problem step by step. We are given: (3x + 7) + (5x - 4) = ? **

4 (12x - 7) - (8x + 5) = ?

Hint: Remember to distribute the subtraction sign to both terms in the second parentheses before combining like terms.

Show the answer

Answer: 4x - 12

  1. Write the original expression: (12x - 7) - (8x + 5)
  2. Distribute the subtraction sign: 12x - 7 - 8x - 5
  3. Combine like terms for x: 12x - 8x = 4x
  4. Combine constant terms: -7 - 5 = -12
  5. Write the final expression: 4x - 12

The answer is 4x - 12.

5 (12x - 8) - (7x + 5) = ?

Hint: Remember to distribute the negative sign to all terms in the second expression before combining like terms.

Show the answer

Answer: 5x - 13

  1. Write the original expression: (12x - 8) - (7x + 5)
  2. Distribute the negative sign to both terms in the second parentheses: 12x - 8 - 7x - 5
  3. Combine like terms for the x terms: 12x - 7x = 5x
  4. Combine like terms for the constants: -8 - 5 = -13
  5. Write the final simplified expression: 5x - 13

The answer is 5x - 13.

6 (12x - 7) - (5x + 9) = ?

Hint: Remember to distribute the negative sign to all terms in the second expression before combining like terms.

Show the answer

Answer: 7x - 16

  1. Write the original expression: (12x - 7) - (5x + 9)
  2. Distribute the negative sign to the second expression: 12x - 7 - 5x - 9
  3. Combine like terms for x: 12x - 5x = 7x
  4. Combine constant terms: -7 - 9 = -16
  5. Write the final simplified expression: 7x - 16

The answer is 7x - 16.

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