Free Algebra Worksheets pdf downloads. Algebra order of operations - Free Printable

Let’s solve each problem step by step.

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Simplify each expression (use distributive property):

1. 2(x + 4)
→ Multiply 2 by x → 2x
→ Multiply 2 by 4 → 8
→ Answer: 2x + 8

2. 4(3x - 4)
→ 4 × 3x = 12x
→ 4 × (-4) = -16
→ Answer: 12x - 16

3. 5(2x + 3)
→ 5 × 2x = 10x
→ 5 × 3 = 15
→ Answer: 10x + 15

4. 4(3x - 1)
→ 4 × 3x = 12x
→ 4 × (-1) = -4
→ Answer: 12x - 4

5. 3(3 - 2x)
→ 3 × 3 = 9
→ 3 × (-2x) = -6x
→ Answer: 9 - 6x (or -6x + 9 — both are correct, but we’ll keep order as given)

6. 8(2x - 1)
→ 8 × 2x = 16x
→ 8 × (-1) = -8
→ Answer: 16x - 8

7. 4(6x + 9)
→ 4 × 6x = 24x
→ 4 × 9 = 36
→ Answer: 24x + 36

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Solve each equation:

8. 2 - x = 4
→ Subtract 2 from both sides: -x = 2
→ Multiply both sides by -1: x = -2
→ Check: 2 - (-2) = 2 + 2 = 4 ✔
→ Answer: x = -2

9. x + 4 = 9
→ Subtract 4 from both sides: x = 5
→ Check: 5 + 4 = 9 ✔
→ Answer: x = 5

10. x - 10 = 12
→ Add 10 to both sides: x = 22
→ Check: 22 - 10 = 12 ✔
→ Answer: x = 22

11. 2x + 2 = 10
→ Subtract 2: 2x = 8
→ Divide by 2: x = 4
→ Check: 2×4 + 2 = 8 + 2 = 10 ✔
→ Answer: x = 4

12. 3x - 12 = 12
→ Add 12: 3x = 24
→ Divide by 3: x = 8
→ Check: 3×8 - 12 = 24 - 12 = 12 ✔
→ Answer: x = 8

13. 6x + 5 = 23
→ Subtract 5: 6x = 18
→ Divide by 6: x = 3
→ Check: 6×3 + 5 = 18 + 5 = 23 ✔
→ Answer: x = 3

14. 9x - 6 = 24
→ Add 6: 9x = 30
→ Divide by 9: x = 30/9 = 10/3 ≈ 3.333...
But let’s leave it as a fraction unless told otherwise.
→ Simplify 30/9: divide numerator and denominator by 3 → 10/3
→ Check: 9×(10/3) - 6 = 30 - 6 = 24 ✔
→ Answer: x = 10/3

*(Note: If decimals are allowed, you can write 3.33 or 3.\overline{3}, but since this is pre-algebra, fractional form is preferred.)*

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Final Answer:

1. 2x + 8
2. 12x - 16
3. 10x + 15
4. 12x - 4
5. 9 - 6x
6. 16x - 8
7. 24x + 36
8. x = -2
9. x = 5
10. x = 22
11. x = 4
12. x = 8
13. x = 3
14. x = 10/3