Subtracting Linear Expressions worksheet - Free Printable

Let's solve the problems in your image step by step.

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Lesson 7 Skills Practice: Subtract Linear Expressions

We are asked to subtract linear expressions. The general rule is:

> To subtract two expressions, distribute the negative sign to each term in the second expression and then combine like terms.

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Problems 1–20: Subtract Linear Expressions

#### 1. $ (5x + 7) - (x + 2) $

Distribute the negative:
$$
5x + 7 - x - 2 = (5x - x) + (7 - 2) = 4x + 5
$$

✔ Answer: $ 4x + 5 $

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#### 2. $ (2x - 6) - (x - 7) $

Distribute:
$$
2x - 6 - x + 7 = (2x - x) + (-6 + 7) = x + 1
$$

✔ Answer: $ x + 1 $

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#### 3. $ (x + 12) - (-4x + 2) $

Distribute:
$$
x + 12 + 4x - 2 = (x + 4x) + (12 - 2) = 5x + 10
$$

✔ Answer: $ 5x + 10 $

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#### 4. $ (5x + 3) - (-7x - 1) $

Distribute:
$$
5x + 3 + 7x + 1 = (5x + 7x) + (3 + 1) = 12x + 4
$$

✔ Answer: $ 12x + 4 $

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#### 5. $ (x + 3) - (4x - 10) $

Distribute:
$$
x + 3 - 4x + 10 = (x - 4x) + (3 + 10) = -3x + 13
$$

✔ Answer: $ -3x + 13 $

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#### 6. $ (5x + 4) - (-4x - 2) $

Distribute:
$$
5x + 4 + 4x + 2 = (5x + 4x) + (4 + 2) = 9x + 6
$$

✔ Answer: $ 9x + 6 $

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#### 7. $ (-7x + 1) - (-6x - 5) $

Distribute:
$$
-7x + 1 + 6x + 5 = (-7x + 6x) + (1 + 5) = -x + 6
$$

✔ Answer: $ -x + 6 $

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#### 8. $ (6x - 2) - (-x + 5) $

Distribute:
$$
6x - 2 + x - 5 = (6x + x) + (-2 - 5) = 7x - 7
$$

✔ Answer: $ 7x - 7 $

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#### 9. $ (-9x + 1) - (-7x + 8) $

Distribute:
$$
-9x + 1 + 7x - 8 = (-9x + 7x) + (1 - 8) = -2x - 7
$$

✔ Answer: $ -2x - 7 $

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#### 10. $ (-3x - 9) - (-6x + 8) $

Distribute:
$$
-3x - 9 + 6x - 8 = (-3x + 6x) + (-9 - 8) = 3x - 17
$$

✔ Answer: $ 3x - 17 $

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#### 11. $ (-8x - 12) - (-x - 8) $

Distribute:
$$
-8x - 12 + x + 8 = (-8x + x) + (-12 + 8) = -7x - 4
$$

✔ Answer: $ -7x - 4 $

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#### 12. $ (14x + 7) - (-3x + 2) $

Distribute:
$$
14x + 7 + 3x - 2 = (14x + 3x) + (7 - 2) = 17x + 5
$$

✔ Answer: $ 17x + 5 $

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#### 13. $ (5x - 1) - (-3x + 7) $

Distribute:
$$
5x - 1 + 3x - 7 = (5x + 3x) + (-1 - 7) = 8x - 8
$$

✔ Answer: $ 8x - 8 $

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#### 14. $ (-5x + 4) - (-9x - 2) $

Distribute:
$$
-5x + 4 + 9x + 2 = (-5x + 9x) + (4 + 2) = 4x + 6
$$

✔ Answer: $ 4x + 6 $

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#### 15. $ (11x + 2) - (-8x - 2) $

Distribute:
$$
11x + 2 + 8x + 2 = (11x + 8x) + (2 + 2) = 19x + 4
$$

✔ Answer: $ 19x + 4 $

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#### 16. $ (-9x - 10) - (-5x - 4) $

Distribute:
$$
-9x - 10 + 5x + 4 = (-9x + 5x) + (-10 + 4) = -4x - 6
$$

✔ Answer: $ -4x - 6 $

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#### 17. $ (x - 2) - (x - 6) $

Distribute:
$$
x - 2 - x + 6 = (x - x) + (-2 + 6) = 0x + 4 = 4
$$

✔ Answer: $ 4 $

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#### 18. $ (-6x + 1) - (-x + 5) $

Distribute:
$$
-6x + 1 + x - 5 = (-6x + x) + (1 - 5) = -5x - 4
$$

✔ Answer: $ -5x - 4 $

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#### 19. $ (2x + 4) - (5x - 2) $

Distribute:
$$
2x + 4 - 5x + 2 = (2x - 5x) + (4 + 2) = -3x + 6
$$

✔ Answer: $ -3x + 6 $

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#### 20. $ (-12x - 6) - (-4x + 5) $

Distribute:
$$
-12x - 6 + 4x - 5 = (-12x + 4x) + (-6 - 5) = -8x - 11
$$

✔ Answer: $ -8x - 11 $

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Problem 21: Geometry – Find the missing side

> The perimeter of the triangle shown is $ 10x + 11 $ feet. Find the length of the missing side.

From the diagram:
- One side: $ x $
- Another side: $ (2x + 6) $ ft
- Third side: $ (5x - 2) $ ft

Let’s call the missing side $ y $. But wait — looking at the diagram, it seems all three sides are labeled, but one might be missing?

Wait — let's re-express what we see:

The triangle has:
- Side A: $ x $
- Side B: $ (2x + 6) $
- Side C: $ (5x - 2) $

But the problem says "find the length of the missing side", so likely one side is not labeled, but based on the image description, it appears that three sides are labeled, including one as $ x $, another as $ 2x + 6 $, and the third as $ 5x - 2 $? Wait — actually, the diagram shows:

- One side: $ x $
- One side: $ (2x + 6) $
- One side: $ (5x - 2) $

Wait — that would mean all three sides are labeled. But the problem says “find the missing side”, so perhaps only two sides are labeled? Let's re-analyze.

Looking at the image text:

> "The perimeter of the triangle shown is $ 10x + 11 $ ft. Find the length of the missing side."

And the diagram shows:
- One side labeled $ x $
- One side labeled $ (2x + 6) $
- One side labeled $ (5x - 2) $ — but this might be the missing one?

Wait — no, it says “the missing side” implies only two are given, and one is unknown.

But in the image, it shows:
- One side: $ x $
- One side: $ (2x + 6) $
- One side: $ ? $ (not labeled)

Wait — actually, from your description:

> "The perimeter of the triangle shown is $ 10x + 11 $ ft. Find the length of the missing side."

And the diagram shows:
- One side: $ x $
- One side: $ (2x + 6) $
- One side: $ (5x - 2) $

But if all three are labeled, why ask for the missing one?

Ah! Wait — maybe the third side is unlabeled, and the other two are $ x $ and $ 2x + 6 $, and the third is $ (5x - 2) $? That doesn't make sense.

Alternatively, perhaps the side labeled $ (5x - 2) $ is not a side — maybe it's a typo.

Wait — let me re-read:

> "The perimeter of the triangle shown is $ 10x + 11 $ ft. Find the length of the missing side."

And the diagram shows:
- One side: $ x $
- One side: $ (2x + 6) $
- One side: $ ? $ (missing)

But you wrote: "(5x - 2) ft" — is that one of the known sides?

Possibility: Maybe the triangle has:
- Side 1: $ x $
- Side 2: $ 2x + 6 $
- Side 3: Unknown → let’s call it $ s $

Perimeter = sum of all sides:
$$
x + (2x + 6) + s = 10x + 11
$$

Solve for $ s $:

$$
x + 2x + 6 + s = 10x + 11 \\
3x + 6 + s = 10x + 11 \\
s = 10x + 11 - 3x - 6 \\
s = 7x + 5
$$

✔ So the missing side is $ \boxed{7x + 5} $ feet.

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✔ Final Answer for Problem 21: $ \boxed{7x + 5} $ feet

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Summary of Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ 4x + 5 $ |
| 2 | $ x + 1 $ |
| 3 | $ 5x + 10 $ |
| 4 | $ 12x + 4 $ |
| 5 | $ -3x + 13 $ |
| 6 | $ 9x + 6 $ |
| 7 | $ -x + 6 $ |
| 8 | $ 7x - 7 $ |
| 9 | $ -2x - 7 $ |
| 10 | $ 3x - 17 $ |
| 11 | $ -7x - 4 $ |
| 12 | $ 17x + 5 $ |
| 13 | $ 8x - 8 $ |
| 14 | $ 4x + 6 $ |
| 15 | $ 19x + 4 $ |
| 16 | $ -4x - 6 $ |
| 17 | $ 4 $ |
| 18 | $ -5x - 4 $ |
| 19 | $ -3x + 6 $ |
| 20 | $ -8x - 11 $ |
| 21 | $ \boxed{7x + 5} $ |

Let me know if you'd like these explained further or want a visual guide!