Algebra Examples

$\frac{x}{5} + \frac{x - 1}{3} = 2$

Step 1

Simplify $\frac{x}{5} + \frac{x - 1}{3}$ .

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Step 1.1

To write $\frac{x}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x}{5} \cdot \frac{3}{3} + \frac{x - 1}{3} = 2$

Step 1.2

To write $\frac{x - 1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x}{5} \cdot \frac{3}{3} + \frac{x - 1}{3} \cdot \frac{5}{5} = 2$

Step 1.3

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{x}{5}$ by $\frac{3}{3}$ .

$\frac{x \cdot 3}{5 \cdot 3} + \frac{x - 1}{3} \cdot \frac{5}{5} = 2$

Step 1.3.2

Multiply $5$ by $3$ .

$\frac{x \cdot 3}{15} + \frac{x - 1}{3} \cdot \frac{5}{5} = 2$

Step 1.3.3

Multiply $\frac{x - 1}{3}$ by $\frac{5}{5}$ .

$\frac{x \cdot 3}{15} + \frac{(x - 1) \cdot 5}{3 \cdot 5} = 2$

Step 1.3.4

Multiply $3$ by $5$ .

$\frac{x \cdot 3}{15} + \frac{(x - 1) \cdot 5}{15} = 2$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x \cdot 3 + (x - 1) \cdot 5}{15} = 2$

Step 1.5

Simplify the numerator.

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Step 1.5.1

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

$\frac{3 \cdot x + (x - 1) \cdot 5}{15} = 2$

Step 1.5.2

Apply the distributive property.

$\frac{3 x + x \cdot 5 - 1 \cdot 5}{15} = 2$

Step 1.5.3

Move $5$ to the left of $x$ .

$\frac{3 x + 5 \cdot x - 1 \cdot 5}{15} = 2$

Step 1.5.4

Multiply $- 1$ by $5$ .

$\frac{3 x + 5 \cdot x - 5}{15} = 2$

Step 1.5.5

Add $3 x$ and $5 x$ .

$\frac{8 x - 5}{15} = 2$

Step 2

Multiply both sides by $15$ .

$\frac{8 x - 5}{15} \cdot 15 = 2 \cdot 15$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $15$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{8 x - 5}{15} \cdot 15 = 2 \cdot 15$

Step 3.1.1.2

Rewrite the expression.

$8 x - 5 = 2 \cdot 15$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $2$ by $15$ .

$8 x - 5 = 30$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Add $5$ to both sides of the equation.

$8 x = 30 + 5$

Step 4.1.2

Add $30$ and $5$ .

$8 x = 35$

Step 4.2

Divide each term in $8 x = 35$ by $8$ and simplify.

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Step 4.2.1

Divide each term in $8 x = 35$ by $8$ .

$\frac{8 x}{8} = \frac{35}{8}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $8$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{35}{8}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{35}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{35}{8}$

Decimal Form:

$x = 4.375$

Mixed Number Form:

$x = 4 \frac{3}{8}$