Adding and Subtracting Linear Expressions Notes and Activity | TPT - Free Printable

Let's solve each of these problems step by step. The key concept here is subtracting linear expressions, which involves distributing the negative sign across the second expression and then combining like terms.

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Problem 6:

(6x + 5) − (3x + 1)

Step 1: Distribute the negative sign to each term in the second parentheses:
= 6x + 5 − 3x − 1

Step 2: Combine like terms:
(6x − 3x) + (5 − 1) = 3x + 4

✔ Answer: 3x + 4

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Problem 7:

(-4x − 7) − (-5x − 2)

Step 1: Distribute the negative sign:
= -4x − 7 + 5x + 2
(Note: −(−5x) = +5x, and −(−2) = +2)

Step 2: Combine like terms:
(-4x + 5x) + (−7 + 2) = x − 5

✔ Answer: x − 5

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Problem 8:

(4x − 3) − (2x + 7)

Step 1: Distribute the negative:
= 4x − 3 − 2x − 7

Step 2: Combine like terms:
(4x − 2x) + (−3 − 7) = 2x − 10

✔ Answer: 2x − 10

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Problem 9:

(5x − 4) − (2x + 3)

Step 1: Distribute the negative:
= 5x − 4 − 2x − 3

Step 2: Combine like terms:
(5x − 2x) + (−4 − 3) = 3x − 7

✔ Answer: 3x − 7

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Problem 10:

(-6x − 11) − (-2x − 4)

Step 1: Distribute the negative:
= -6x − 11 + 2x + 4
(Note: −(−2x) = +2x, −(−4) = +4)

Step 2: Combine like terms:
(-6x + 2x) + (−11 + 4) = -4x − 7

✔ Answer: -4x − 7

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✔ Final Answers:

6. 3x + 4
7. x − 5
8. 2x − 10
9. 3x − 7
10. -4x − 7

Let me know if you'd like a visual explanation or practice with more examples!