Linear Equations in One Variable online worksheet - Free Printable

Of course! Let's solve each of these linear equations in one variable step by step. The goal is to isolate the variable on one side of the equation.

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1. $ x - 2 = 7 $

To isolate $x$, add 2 to both sides:

$ x - 2 + 2 = 7 + 2 $

$ x = 9 $

✔ Answer: 9

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2. $ y + 3 = 10 $

Subtract 3 from both sides:

$ y + 3 - 3 = 10 - 3 $

$ y = 7 $

✔ Answer: 7

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3. $ 6 = z + 2 $

Subtract 2 from both sides:

$ 6 - 2 = z + 2 - 2 $

$ 4 = z $

✔ Answer: 4

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4. $ \frac{3}{7} + x = \frac{17}{7} $

Subtract $\frac{3}{7}$ from both sides:

$ x = \frac{17}{7} - \frac{3}{7} = \frac{14}{7} = 2 $

✔ Answer: 2

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5. $ 6x = 12 $

Divide both sides by 6:

$ x = \frac{12}{6} = 2 $

✔ Answer: 2

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6. $ \frac{t}{5} = 10 $

Multiply both sides by 5:

$ t = 10 \times 5 = 50 $

✔ Answer: 50

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7. $ \frac{2x}{3} = 18 $

Multiply both sides by 3 to eliminate the denominator:

$ 2x = 18 \times 3 = 54 $

Now divide both sides by 2:

$ x = \frac{54}{2} = 27 $

✔ Answer: 27

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8. $ 1.6 = \frac{y}{1.5} $

Multiply both sides by 1.5:

$ y = 1.6 \times 1.5 $

Calculate: $ 1.6 \times 1.5 = (1.6 \times 1) + (1.6 \times 0.5) = 1.6 + 0.8 = 2.4 $

✔ Answer: 2.4

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9. $ 7x - 9 = 26 $

Add 9 to both sides:

$ 7x = 26 + 9 = 35 $

Divide by 7:

$ x = \frac{35}{7} = 5 $

✔ Answer: 5

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10. $ 14y - 8 = 13 $

Add 8 to both sides:

$ 14y = 13 + 8 = 21 $

Divide by 14:

$ y = \frac{21}{14} = \frac{3}{2} = 1.5 $

✔ Answer: 1.5

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✔ Final Answers:

1. 9
2. 7
3. 4
4. 2
5. 2
6. 50
7. 27
8. 2.4
9. 5
10. 1.5

Let me know if you’d like a printable version or further explanations!