How to Solve an Equation with a Fraction

Step-by-step solution

1. Subtract 2 from both sides to undo the addition.

   $$\frac{x}{3} = 3$$

   Why: Undo addition and subtraction before multiplication and division.

2. Multiply both sides by 3 to clear the fraction.

   $$3 \times \frac{x}{3} = 3 \times 3$$

   Why: Multiplying by the denominator undoes the division.

3. Simplify both sides.

   $$x = 9$$

   Why: The 3s cancel on the left.

4. Check the answer in the original equation.

   $$\frac{9}{3} + 2 = 3 + 2 = 5$$

   Why: The check confirms that the two sides are equal.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

1. 1

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

   Show answer

   $x = 16$

2. 2

   $\frac{x}{5} - 1 = 4$

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   $x = 25$

3. 3

   $\frac{2x}{3} = 8$

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   $x = 12$

4. 4

   $\frac{x}{2} + \frac{x}{3} = 5$

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   $x = 6$

5. 5

   $3 - \frac{x}{4} = 1$

   Show answer

   $x = 8$