Solve for x 1 2/7+2 1/3x+3/14+x=9

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

Step 1

Simplify the left side.

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Add $7$ and $2$ .

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

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

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $3$ .

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

Add $6$ and $1$ .

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

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

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

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

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

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

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

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

Multiply $7$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $9$ by $2$ .

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

Add $18$ and $3$ .

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

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

Factor $7$ out of $21$ .

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

Cancel the common factors.

Factor $7$ out of $14$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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

Combine the numerators over the common denominator.

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

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

Reorder $x$ and $3$ .

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

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.

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $9$ by $2$ .

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

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.

Simplify the left side.

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $10$ .

Factor $10$ out of $10 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

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

Cancel the common factor of $5$ .

Factor $5$ out of $10$ .

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

Factor $5$ out of $15$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Multiply.

Multiply $3$ by $3$ .

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

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:

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

Solve for x 1 2/7+2 1/3x+3/14+x=9

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