Math worksheet featuring ten algebraic equations to solve, designed for practice and learning.

Sure! Let’s solve each of the 10 equations step by step. We’ll isolate the variable on one side and simplify to find its value. Round to the nearest hundredth if needed.

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1) -4k + 3 = 9 - 7k

Add 7k to both sides:
→ 3k + 3 = 9

Subtract 3 from both sides:
→ 3k = 6

Divide by 3:
→ k = 2

✔ Final Answer: k = 2.00

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2) -5 + 3r = -2(9 + 4r)

Distribute the -2 on the right:
→ -5 + 3r = -18 - 8r

Add 8r to both sides:
→ -5 + 11r = -18

Add 5 to both sides:
→ 11r = -13

Divide by 11:
→ r = -13/11 ≈ -1.18

✔ Final Answer: r ≈ -1.18

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3) -6 - 4x = 4x + 5x

Simplify right side:
→ -6 - 4x = 9x

Add 4x to both sides:
→ -6 = 13x

Divide by 13:
→ x = -6/13 ≈ -0.46

✔ Final Answer: x ≈ -0.46

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4) -3s - 9 = 7(-3s + 4)

Distribute the 7:
→ -3s - 9 = -21s + 28

Add 21s to both sides:
→ 18s - 9 = 28

Add 9 to both sides:
→ 18s = 37

Divide by 18:
→ s = 37/18 ≈ 2.06

✔ Final Answer: s ≈ 2.06

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5) -2f - 4f - 8 = -3f + 9

Combine like terms on left:
→ -6f - 8 = -3f + 9

Add 6f to both sides:
→ -8 = 3f + 9

Subtract 9 from both sides:
→ -17 = 3f

Divide by 3:
→ f = -17/3 ≈ -5.67

✔ Final Answer: f ≈ -5.67

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6) -5(-9 - 5d) = 9(6d - 3)

Distribute both sides:

Left: -5 * -9 = 45; -5 * -5d = 25d → 45 + 25d

Right: 9*6d = 54d; 9*-3 = -27 → 54d - 27

So:
→ 45 + 25d = 54d - 27

Subtract 25d from both sides:
→ 45 = 29d - 27

Add 27 to both sides:
→ 72 = 29d

Divide by 29:
→ d = 72/29 ≈ 2.48

✔ Final Answer: d ≈ 2.48

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7) 3h + 5(-9 - 5h) = -3h + 2h

Simplify both sides:

Left: 3h - 45 - 25h = -22h - 45

Right: -3h + 2h = -h

So:
→ -22h - 45 = -h

Add 22h to both sides:
→ -45 = 21h

Divide by 21:
→ h = -45/21 = -15/7 ≈ -2.14

✔ Final Answer: h ≈ -2.14

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8) -2 + 5v = 3(v - 5)

Distribute right side:
→ -2 + 5v = 3v - 15

Subtract 3v from both sides:
→ -2 + 2v = -15

Add 2 to both sides:
→ 2v = -13

Divide by 2:
→ v = -13/2 = -6.5

✔ Final Answer: v = -6.50

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9) 9(y + 2) - 5(y - 6) = -4y - 9

Distribute:

Left: 9y + 18 - 5y + 30 = (9y - 5y) + (18 + 30) = 4y + 48

Right: -4y - 9

So:
→ 4y + 48 = -4y - 9

Add 4y to both sides:
→ 8y + 48 = -9

Subtract 48:
→ 8y = -57

Divide by 8:
→ y = -57/8 = -7.125 → rounded to hundredth: -7.13

✔ Final Answer: y ≈ -7.13

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10) 9 + 5n - 4 + 5 = 4n - 2

Simplify left side:
→ (9 - 4 + 5) + 5n = 10 + 5n

So:
→ 10 + 5n = 4n - 2

Subtract 4n from both sides:
→ 10 + n = -2

Subtract 10:
→ n = -12

✔ Final Answer: n = -12.00

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## ✔ Final Answers Summary:

1) k = 2.00
2) r ≈ -1.18
3) x ≈ -0.46
4) s ≈ 2.06
5) f ≈ -5.67
6) d ≈ 2.48
7) h ≈ -2.14
8) v = -6.50
9) y ≈ -7.13
10) n = -12.00

Let me know if you’d like to see any step explained further!