Pre-Algebra - Equations - One Step Equations Containing Integers Worksheets - Free Printable

Let's go through each part of the problem step by step.

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Part 1: Identify the terms, like terms, coefficients, and constants

We’ll analyze each expression one by one.

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#### 17. $ 3 + 7x + 3x + x $

- Terms: $3$, $7x$, $3x$, $x$
- Like terms: $7x$, $3x$, $x$ (all are $x$-terms)
- Coefficients:
- $7$ (for $7x$),
- $3$ (for $3x$),
- $1$ (for $x$, since $x = 1x$)
- Constants: $3$

> Note: Constants are numbers without variables.

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#### 18. $ y + 3y + 8y + 2 $

- Terms: $y$, $3y$, $8y$, $2$
- Like terms: $y$, $3y$, $8y$ (all are $y$-terms)
- Coefficients:
- $1$ (for $y$),
- $3$ (for $3y$),
- $8$ (for $8y$)
- Constants: $2$

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#### 19. $ 2a + 5c - a + 6a $

- Terms: $2a$, $5c$, $-a$, $6a$
- Like terms: $2a$, $-a$, $6a$ (all are $a$-terms); $5c$ is alone
- Coefficients:
- $2$ (for $2a$),
- $5$ (for $5c$),
- $-1$ (for $-a$),
- $6$ (for $6a$)
- Constants: None

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#### 20. $ 5c - 2d + 3d - d $

- Terms: $5c$, $-2d$, $3d$, $-d$
- Like terms: $-2d$, $3d$, $-d$ (all are $d$-terms); $5c$ is alone
- Coefficients:
- $5$ (for $5c$),
- $-2$ (for $-2d$),
- $3$ (for $3d$),
- $-1$ (for $-d$)
- Constants: None

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#### 21. $ 6m - 2n + 7 $

- Terms: $6m$, $-2n$, $7$
- Like terms: None — all different variables or constant
- Coefficients:
- $6$ (for $6m$),
- $-2$ (for $-2n$)
- Constants: $7$

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#### 22. $ 7x - 3y + 3z - 2 $

- Terms: $7x$, $-3y$, $3z$, $-2$
- Like terms: None — all different variables
- Coefficients:
- $7$ (for $7x$),
- $-3$ (for $-3y$),
- $3$ (for $3z$)
- Constants: $-2$

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Part 2: Simplify each expression

Now we simplify by combining like terms.

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#### 23. $ 2x + 5x = 7x $

- Like terms: both have $x$
- $2 + 5 = 7$ → $7x$

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#### 24. $ 7b + 2b = 9b $

- $7 + 2 = 9$ → $9b$

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#### 25. $ y + 10y = 11y $

- $1 + 10 = 11$ → $11y$

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#### 26. $ 5y + y = 6y $

- $5 + 1 = 6$ → $6y$

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#### 27. $ 2a + 3 + 5a = (2a + 5a) + 3 = 7a + 3 $

- Combine $a$-terms: $2a + 5a = 7a$

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#### 28. $ 4 + 2m + m = 4 + (2m + m) = 4 + 3m $

- Combine $m$-terms: $2m + m = 3m$

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#### 29. $ 2y + 8 + 5y + 1 = (2y + 5y) + (8 + 1) = 7y + 9 $

- Combine $y$: $2y + 5y = 7y$; constants: $8 + 1 = 9$

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#### 30. $ 8x + 5 + 7 + 2x = (8x + 2x) + (5 + 7) = 10x + 12 $

- $x$-terms: $8x + 2x = 10x$; constants: $5 + 7 = 12$

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#### 31. $ 5x - 3x = 2x $

- $5 - 3 = 2$ → $2x$

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#### 32. $ 10b - 2b = 8b $

- $10 - 2 = 8$ → $8b$

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#### 33. $ 4y - 5y = -y $

- $4 - 5 = -1$ → $-y$

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#### 34. $ r - 3r = -2r $

- $1r - 3r = -2r$

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#### 35. $ 8 + x - 5x = 8 + (x - 5x) = 8 - 4x $

- $x - 5x = -4x$

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#### 36. $ 6x + 4 - 7x = (6x - 7x) + 4 = -x + 4 $

- $6x - 7x = -x$

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#### 37. $ 8y - 7 + 7 = 8y + 0 = 8y $

- $-7 + 7 = 0$, so only $8y$ remains

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#### 38. $ 9x + 2 - 2 = 9x + 0 = 9x $

- $2 - 2 = 0$

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#### 39. $ 2x + 3 - 3x + 9 = (2x - 3x) + (3 + 9) = -x + 12 $

- $x$-terms: $2x - 3x = -x$; constants: $3 + 9 = 12$

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#### 40. $ 5t - 3 - t + 2 = (5t - t) + (-3 + 2) = 4t - 1 $

- $t$-terms: $5t - t = 4t$; constants: $-3 + 2 = -1$

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#### 41. $ 3(b + 2) + 2b $

- First distribute: $3 \cdot b = 3b$, $3 \cdot 2 = 6$ → $3b + 6 + 2b$
- Combine: $3b + 2b = 5b$ → $5b + 6$

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#### 42. $ 5(x + 3) + 8x $

- Distribute: $5x + 15 + 8x$
- Combine: $5x + 8x = 13x$ → $13x + 15$

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#### 43. $ -3(a + 2) - a $

- Distribute: $-3a - 6 - a$
- Combine: $-3a - a = -4a$ → $-4a - 6$

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#### 44. $ -2(x + 3) + 2x $

- Distribute: $-2x - 6 + 2x$
- Combine: $-2x + 2x = 0$ → $-6$

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#### 45. $ 4x - 4(2 + x) $

- Distribute: $4x - 8 - 4x$
- Combine: $4x - 4x = 0$ → $-8$

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#### 46. $ 8a - 2(a - 7) $

- Distribute: $8a - 2a + 14 = 6a + 14$

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#### 47. $ 6m + 2n + 10m $

- Combine $m$-terms: $6m + 10m = 16m$ → $16m + 2n$

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#### 48. $ -2y + x + 3y $

- Combine $y$-terms: $-2y + 3y = y$ → $x + y$

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#### 49. $ c + 2(d - 5c) $

- Distribute: $c + 2d - 10c$
- Combine $c$-terms: $c - 10c = -9c$ → $-9c + 2d$

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✔ Final Answers:

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#### Identify Terms, Like Terms, Coefficients, Constants

| Problem | Terms | Like Terms | Coefficients | Constants |
|--------|-------|------------|--------------|-----------|
| 17 | $3, 7x, 3x, x$ | $7x, 3x, x$ | $7, 3, 1$ | $3$ |
| 18 | $y, 3y, 8y, 2$ | $y, 3y, 8y$ | $1, 3, 8$ | $2$ |
| 19 | $2a, 5c, -a, 6a$ | $2a, -a, 6a$ | $2, 5, -1, 6$ | none |
| 20 | $5c, -2d, 3d, -d$ | $-2d, 3d, -d$ | $5, -2, 3, -1$ | none |
| 21 | $6m, -2n, 7$ | none | $6, -2$ | $7$ |
| 22 | $7x, -3y, 3z, -2$ | none | $7, -3, 3$ | $-2$ |

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#### Simplify Each Expression

| Problem | Simplified |
|--------|------------|
| 23 | $7x$ |
| 24 | $9b$ |
| 25 | $11y$ |
| 26 | $6y$ |
| 27 | $7a + 3$ |
| 28 | $3m + 4$ |
| 29 | $7y + 9$ |
| 30 | $10x + 12$ |
| 31 | $2x$ |
| 32 | $8b$ |
| 33 | $-y$ |
| 34 | $-2r$ |
| 35 | $8 - 4x$ |
| 36 | $-x + 4$ |
| 37 | $8y$ |
| 38 | $9x$ |
| 39 | $-x + 12$ |
| 40 | $4t - 1$ |
| 41 | $5b + 6$ |
| 42 | $13x + 15$ |
| 43 | $-4a - 6$ |
| 44 | $-6$ |
| 45 | $-8$ |
| 46 | $6a + 14$ |
| 47 | $16m + 2n$ |
| 48 | $x + y$ |
| 49 | $-9c + 2d$ |

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