Algebra Examples

$1 \frac{2}{7} + 2 \frac{1}{3} x + \frac{3}{14} + x = 9$

Step 1

Simplify the left side.

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Step 1.1

Simplify $1 \frac{2}{7} + 2 \frac{1}{3} x + \frac{3}{14} + x$ .

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Step 1.1.1

Convert $1 \frac{2}{7}$ to an improper fraction.

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Step 1.1.1.1

A mixed number is an addition of its whole and fractional parts.

$1 + \frac{2}{7} + 2 \frac{1}{3} x + \frac{3}{14} + x = 9$

Step 1.1.1.2

Add $1$ and $\frac{2}{7}$ .

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Step 1.1.1.2.1

Write $1$ as a fraction with a common denominator.

$\frac{7}{7} + \frac{2}{7} + 2 \frac{1}{3} x + \frac{3}{14} + x = 9$

Step 1.1.1.2.2

Combine the numerators over the common denominator.

$\frac{7 + 2}{7} + 2 \frac{1}{3} x + \frac{3}{14} + x = 9$

Step 1.1.1.2.3

Add $7$ and $2$ .

$\frac{9}{7} + 2 \frac{1}{3} x + \frac{3}{14} + x = 9$

Step 1.1.2

Convert $2 \frac{1}{3}$ to an improper fraction.

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Step 1.1.2.1

A mixed number is an addition of its whole and fractional parts.

$\frac{9}{7} + (2 + \frac{1}{3}) x + \frac{3}{14} + x = 9$

Step 1.1.2.2

Add $2$ and $\frac{1}{3}$ .

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Step 1.1.2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{9}{7} + (2 \cdot \frac{3}{3} + \frac{1}{3}) x + \frac{3}{14} + x = 9$

Step 1.1.2.2.2

Combine $2$ and $\frac{3}{3}$ .

$\frac{9}{7} + (\frac{2 \cdot 3}{3} + \frac{1}{3}) x + \frac{3}{14} + x = 9$

Step 1.1.2.2.3

Combine the numerators over the common denominator.

$\frac{9}{7} + \frac{2 \cdot 3 + 1}{3} x + \frac{3}{14} + x = 9$

Step 1.1.2.2.4

Simplify the numerator.

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Step 1.1.2.2.4.1

Multiply $2$ by $3$ .

$\frac{9}{7} + \frac{6 + 1}{3} x + \frac{3}{14} + x = 9$

Step 1.1.2.2.4.2

Add $6$ and $1$ .

$\frac{9}{7} + \frac{7}{3} x + \frac{3}{14} + x = 9$

Step 1.1.3

Combine $\frac{7}{3}$ and $x$ .

$\frac{9}{7} + \frac{7 x}{3} + \frac{3}{14} + x = 9$

Step 1.1.4

To write $\frac{9}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{7 x}{3} + \frac{9}{7} \cdot \frac{2}{2} + \frac{3}{14} + x = 9$

Step 1.1.5

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.1.5.1

Multiply $\frac{9}{7}$ by $\frac{2}{2}$ .

$\frac{7 x}{3} + \frac{9 \cdot 2}{7 \cdot 2} + \frac{3}{14} + x = 9$

Step 1.1.5.2

Multiply $7$ by $2$ .

$\frac{7 x}{3} + \frac{9 \cdot 2}{14} + \frac{3}{14} + x = 9$

Step 1.1.6

Combine the numerators over the common denominator.

$\frac{7 x}{3} + \frac{9 \cdot 2 + 3}{14} + x = 9$

Step 1.1.7

Simplify the numerator.

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Step 1.1.7.1

Multiply $9$ by $2$ .

$\frac{7 x}{3} + \frac{18 + 3}{14} + x = 9$

Step 1.1.7.2

Add $18$ and $3$ .

$\frac{7 x}{3} + \frac{21}{14} + x = 9$

Step 1.1.8

Cancel the common factor of $21$ and $14$ .

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Step 1.1.8.1

Factor $7$ out of $21$ .

$\frac{7 x}{3} + \frac{7 (3)}{14} + x = 9$

Step 1.1.8.2

Cancel the common factors.

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Step 1.1.8.2.1

Factor $7$ out of $14$ .

$\frac{7 x}{3} + \frac{7 \cdot 3}{7 \cdot 2} + x = 9$

Step 1.1.8.2.2

Cancel the common factor.

$\frac{7 x}{3} + \frac{7 \cdot 3}{7 \cdot 2} + x = 9$

Step 1.1.8.2.3

Rewrite the expression.

$\frac{7 x}{3} + \frac{3}{2} + x = 9$

Step 1.1.9

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

$\frac{7 x}{3} + x \cdot \frac{3}{3} + \frac{3}{2} = 9$

Step 1.1.10

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

$\frac{7 x}{3} + \frac{x \cdot 3}{3} + \frac{3}{2} = 9$

Step 1.1.11

Combine the numerators over the common denominator.

$\frac{7 x + x \cdot 3}{3} + \frac{3}{2} = 9$

Step 1.1.12

Add $7 x$ and $x \cdot 3$ .

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Step 1.1.12.1

Reorder $x$ and $3$ .

$\frac{7 x + 3 \cdot x}{3} + \frac{3}{2} = 9$

Step 1.1.12.2

Add $7 x$ and $3 \cdot x$ .

$\frac{10 x}{3} + \frac{3}{2} = 9$

Step 2

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

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Step 2.1

Subtract $\frac{3}{2}$ from both sides of the equation.

$\frac{10 x}{3} = 9 - \frac{3}{2}$

Step 2.2

To write $9$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{10 x}{3} = 9 \cdot \frac{2}{2} - \frac{3}{2}$

Step 2.3

Combine $9$ and $\frac{2}{2}$ .

$\frac{10 x}{3} = \frac{9 \cdot 2}{2} - \frac{3}{2}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{10 x}{3} = \frac{9 \cdot 2 - 3}{2}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $9$ by $2$ .

$\frac{10 x}{3} = \frac{18 - 3}{2}$

Step 2.5.2

Subtract $3$ from $18$ .

$\frac{10 x}{3} = \frac{15}{2}$

Step 3

Multiply both sides of the equation by $\frac{3}{10}$ .

$\frac{3}{10} \cdot \frac{10 x}{3} = \frac{3}{10} \cdot \frac{15}{2}$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{3}{10} \cdot \frac{10 x}{3}$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{3}{10} \cdot \frac{10 x}{3} = \frac{3}{10} \cdot \frac{15}{2}$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{10} (10 x) = \frac{3}{10} \cdot \frac{15}{2}$

Step 4.1.1.2

Cancel the common factor of $10$ .

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Step 4.1.1.2.1

Factor $10$ out of $10 x$ .

$\frac{1}{10} (10 (x)) = \frac{3}{10} \cdot \frac{15}{2}$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{10} (10 x) = \frac{3}{10} \cdot \frac{15}{2}$

Step 4.1.1.2.3

Rewrite the expression.

$x = \frac{3}{10} \cdot \frac{15}{2}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{3}{10} \cdot \frac{15}{2}$ .

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Step 4.2.1.1

Cancel the common factor of $5$ .

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Step 4.2.1.1.1

Factor $5$ out of $10$ .

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

Step 4.2.1.1.2

Factor $5$ out of $15$ .

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

Step 4.2.1.1.3

Cancel the common factor.

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

Step 4.2.1.1.4

Rewrite the expression.

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

Step 4.2.1.2

Multiply $\frac{3}{2}$ by $\frac{3}{2}$ .

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

Step 4.2.1.3

Multiply.

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Step 4.2.1.3.1

Multiply $3$ by $3$ .

$x = \frac{9}{2 \cdot 2}$

Step 4.2.1.3.2

Multiply $2$ by $2$ .

$x = \frac{9}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9}{4}$

Decimal Form:

$x = 2.25$

Mixed Number Form:

$x = 2 \frac{1}{4}$