Algebra Examples

$3 + \frac{x}{5} = \frac{x + 1}{3}$

Step 1

Multiply both sides by $3$ .

$(3 + \frac{x}{5}) \cdot 3 = \frac{x + 1}{3} \cdot 3$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(3 + \frac{x}{5}) \cdot 3$ .

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Step 2.1.1.1

Simplify terms.

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Step 2.1.1.1.1

Apply the distributive property.

$3 \cdot 3 + \frac{x}{5} \cdot 3 = \frac{x + 1}{3} \cdot 3$

Step 2.1.1.1.2

Multiply $3$ by $3$ .

$9 + \frac{x}{5} \cdot 3 = \frac{x + 1}{3} \cdot 3$

Step 2.1.1.1.3

Combine $\frac{x}{5}$ and $3$ .

$9 + \frac{x \cdot 3}{5} = \frac{x + 1}{3} \cdot 3$

Step 2.1.1.2

Move $3$ to the left of $x$ .

$9 + \frac{3 x}{5} = \frac{x + 1}{3} \cdot 3$

Step 2.1.1.3

Reorder $9$ and $\frac{3 x}{5}$ .

$\frac{3 x}{5} + 9 = \frac{x + 1}{3} \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 x}{5} + 9 = \frac{x + 1}{3} \cdot 3$

Step 2.2.1.2

Rewrite the expression.

$\frac{3 x}{5} + 9 = x + 1$

Step 3

Solve for $x$ .

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Step 3.1

Move all terms containing $x$ to the left side of the equation.

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Step 3.1.1

Subtract $x$ from both sides of the equation.

$\frac{3 x}{5} + 9 - x = 1$

Step 3.1.2

To write $- x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3 x}{5} - x \cdot \frac{5}{5} + 9 = 1$

Step 3.1.3

Combine $- x$ and $\frac{5}{5}$ .

$\frac{3 x}{5} + \frac{- x \cdot 5}{5} + 9 = 1$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{3 x - x \cdot 5}{5} + 9 = 1$

Step 3.1.5

Simplify each term.

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Step 3.1.5.1

Simplify the numerator.

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Step 3.1.5.1.1

Factor $x$ out of $3 x - x \cdot 5$ .

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Step 3.1.5.1.1.1

Factor $x$ out of $3 x$ .

$\frac{x \cdot 3 - x \cdot 5}{5} + 9 = 1$

Step 3.1.5.1.1.2

Factor $x$ out of $- x \cdot 5$ .

$\frac{x \cdot 3 + x (- 1 \cdot 5)}{5} + 9 = 1$

Step 3.1.5.1.1.3

Factor $x$ out of $x \cdot 3 + x (- 1 \cdot 5)$ .

$\frac{x (3 - 1 \cdot 5)}{5} + 9 = 1$

Step 3.1.5.1.2

Multiply $- 1$ by $5$ .

$\frac{x (3 - 5)}{5} + 9 = 1$

Step 3.1.5.1.3

Subtract $5$ from $3$ .

$\frac{x \cdot - 2}{5} + 9 = 1$

Step 3.1.5.2

Move $- 2$ to the left of $x$ .

$\frac{- 2 \cdot x}{5} + 9 = 1$

Step 3.1.5.3

Move the negative in front of the fraction.

$- \frac{2 x}{5} + 9 = 1$

Step 3.2

Move all terms not containing $x$ to the right side of the equation.

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Step 3.2.1

Subtract $9$ from both sides of the equation.

$- \frac{2 x}{5} = 1 - 9$

Step 3.2.2

Subtract $9$ from $1$ .

$- \frac{2 x}{5} = - 8$

Step 3.3

Multiply both sides of the equation by $- \frac{5}{2}$ .

$- \frac{5}{2} (- \frac{2 x}{5}) = - \frac{5}{2} \cdot - 8$

Step 3.4

Simplify both sides of the equation.

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Step 3.4.1

Simplify the left side.

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Step 3.4.1.1

Simplify $- \frac{5}{2} (- \frac{2 x}{5})$ .

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Step 3.4.1.1.1

Cancel the common factor of $5$ .

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Step 3.4.1.1.1.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$\frac{- 5}{2} (- \frac{2 x}{5}) = - \frac{5}{2} \cdot - 8$

Step 3.4.1.1.1.2

Move the leading negative in $- \frac{2 x}{5}$ into the numerator.

$\frac{- 5}{2} \cdot \frac{- 2 x}{5} = - \frac{5}{2} \cdot - 8$

Step 3.4.1.1.1.3

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{2} \cdot \frac{- 2 x}{5} = - \frac{5}{2} \cdot - 8$

Step 3.4.1.1.1.4

Cancel the common factor.

$\frac{5 \cdot - 1}{2} \cdot \frac{- 2 x}{5} = - \frac{5}{2} \cdot - 8$

Step 3.4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{2} (- 2 x) = - \frac{5}{2} \cdot - 8$

Step 3.4.1.1.2

Cancel the common factor of $2$ .

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Step 3.4.1.1.2.1

Factor $2$ out of $- 2 x$ .

$\frac{- 1}{2} (2 (- x)) = - \frac{5}{2} \cdot - 8$

Step 3.4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{2} (2 (- x)) = - \frac{5}{2} \cdot - 8$

Step 3.4.1.1.2.3

Rewrite the expression.

$- - x = - \frac{5}{2} \cdot - 8$

Step 3.4.1.1.3

Multiply.

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Step 3.4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{5}{2} \cdot - 8$

Step 3.4.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{5}{2} \cdot - 8$

Step 3.4.2

Simplify the right side.

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Step 3.4.2.1

Simplify $- \frac{5}{2} \cdot - 8$ .

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Step 3.4.2.1.1

Cancel the common factor of $2$ .

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Step 3.4.2.1.1.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$x = \frac{- 5}{2} \cdot - 8$

Step 3.4.2.1.1.2

Factor $2$ out of $- 8$ .

$x = \frac{- 5}{2} \cdot (2 (- 4))$

Step 3.4.2.1.1.3

Cancel the common factor.

$x = \frac{- 5}{2} \cdot (2 \cdot - 4)$

Step 3.4.2.1.1.4

Rewrite the expression.

$x = - 5 \cdot - 4$

Step 3.4.2.1.2

Multiply $- 5$ by $- 4$ .

$x = 20$