Algebra Examples

$\frac{3 x + 9}{2} + \frac{x + 1}{5} = x + 4$

Step 1

Simplify $\frac{3 x + 9}{2} + \frac{x + 1}{5}$ .

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Step 1.1

Factor $3$ out of $3 x + 9$ .

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Step 1.1.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) + 9}{2} + \frac{x + 1}{5} = x + 4$

Step 1.1.2

Factor $3$ out of $9$ .

$\frac{3 x + 3 \cdot 3}{2} + \frac{x + 1}{5} = x + 4$

Step 1.1.3

Factor $3$ out of $3 x + 3 \cdot 3$ .

$\frac{3 (x + 3)}{2} + \frac{x + 1}{5} = x + 4$

Step 1.2

To write $\frac{3 (x + 3)}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3 (x + 3)}{2} \cdot \frac{5}{5} + \frac{x + 1}{5} = x + 4$

Step 1.3

To write $\frac{x + 1}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 (x + 3)}{2} \cdot \frac{5}{5} + \frac{x + 1}{5} \cdot \frac{2}{2} = x + 4$

Step 1.4

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{3 (x + 3)}{2}$ by $\frac{5}{5}$ .

$\frac{3 (x + 3) \cdot 5}{2 \cdot 5} + \frac{x + 1}{5} \cdot \frac{2}{2} = x + 4$

Step 1.4.2

Multiply $2$ by $5$ .

$\frac{3 (x + 3) \cdot 5}{10} + \frac{x + 1}{5} \cdot \frac{2}{2} = x + 4$

Step 1.4.3

Multiply $\frac{x + 1}{5}$ by $\frac{2}{2}$ .

$\frac{3 (x + 3) \cdot 5}{10} + \frac{(x + 1) \cdot 2}{5 \cdot 2} = x + 4$

Step 1.4.4

Multiply $5$ by $2$ .

$\frac{3 (x + 3) \cdot 5}{10} + \frac{(x + 1) \cdot 2}{10} = x + 4$

Step 1.5

Combine the numerators over the common denominator.

$\frac{3 (x + 3) \cdot 5 + (x + 1) \cdot 2}{10} = x + 4$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Apply the distributive property.

$\frac{(3 x + 3 \cdot 3) \cdot 5 + (x + 1) \cdot 2}{10} = x + 4$

Step 1.6.2

Multiply $3$ by $3$ .

$\frac{(3 x + 9) \cdot 5 + (x + 1) \cdot 2}{10} = x + 4$

Step 1.6.3

Apply the distributive property.

$\frac{3 x \cdot 5 + 9 \cdot 5 + (x + 1) \cdot 2}{10} = x + 4$

Step 1.6.4

Multiply $5$ by $3$ .

$\frac{15 x + 9 \cdot 5 + (x + 1) \cdot 2}{10} = x + 4$

Step 1.6.5

Multiply $9$ by $5$ .

$\frac{15 x + 45 + (x + 1) \cdot 2}{10} = x + 4$

Step 1.6.6

Apply the distributive property.

$\frac{15 x + 45 + x \cdot 2 + 1 \cdot 2}{10} = x + 4$

Step 1.6.7

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

$\frac{15 x + 45 + 2 \cdot x + 1 \cdot 2}{10} = x + 4$

Step 1.6.8

Multiply $2$ by $1$ .

$\frac{15 x + 45 + 2 \cdot x + 2}{10} = x + 4$

Step 1.6.9

Add $15 x$ and $2 x$ .

$\frac{17 x + 45 + 2}{10} = x + 4$

Step 1.6.10

Add $45$ and $2$ .

$\frac{17 x + 47}{10} = x + 4$

Step 2

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

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Step 2.1

Subtract $x$ from both sides of the equation.

$\frac{17 x + 47}{10} - x = 4$

Step 2.2

To write $- x$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{17 x + 47}{10} - x \cdot \frac{10}{10} = 4$

Step 2.3

Combine $- x$ and $\frac{10}{10}$ .

$\frac{17 x + 47}{10} + \frac{- x \cdot 10}{10} = 4$

Step 2.4

Combine the numerators over the common denominator.

$\frac{17 x + 47 - x \cdot 10}{10} = 4$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $10$ by $- 1$ .

$\frac{17 x + 47 - 10 x}{10} = 4$

Step 2.5.2

Subtract $10 x$ from $17 x$ .

$\frac{7 x + 47}{10} = 4$

Step 3

Multiply both sides by $10$ .

$\frac{7 x + 47}{10} \cdot 10 = 4 \cdot 10$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $10$ .

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Step 4.1.1.1

Cancel the common factor.

$\frac{7 x + 47}{10} \cdot 10 = 4 \cdot 10$

Step 4.1.1.2

Rewrite the expression.

$7 x + 47 = 4 \cdot 10$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $4$ by $10$ .

$7 x + 47 = 40$

Step 5

Solve for $x$ .

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Step 5.1

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

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Step 5.1.1

Subtract $47$ from both sides of the equation.

$7 x = 40 - 47$

Step 5.1.2

Subtract $47$ from $40$ .

$7 x = - 7$

Step 5.2

Divide each term in $7 x = - 7$ by $7$ and simplify.

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Step 5.2.1

Divide each term in $7 x = - 7$ by $7$ .

$\frac{7 x}{7} = \frac{- 7}{7}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $7$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 7}{7}$

Step 5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 7}{7}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $- 7$ by $7$ .

$x = - 1$