Solve for x 7 2/5=2/3x-4 1/2

$7 \frac{2}{5} = \frac{2}{3} x - 4 \frac{1}{2}$

Step 1

Simplify the left side.

Convert $7 \frac{2}{5}$ to an improper fraction.

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

$7 + \frac{2}{5} = \frac{2}{3} x - 4 \frac{1}{2}$

Add $7$ and $\frac{2}{5}$ .

To write $7$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$7 \cdot \frac{5}{5} + \frac{2}{5} = \frac{2}{3} x - 4 \frac{1}{2}$

Combine $7$ and $\frac{5}{5}$ .

$\frac{7 \cdot 5}{5} + \frac{2}{5} = \frac{2}{3} x - 4 \frac{1}{2}$

Combine the numerators over the common denominator.

$\frac{7 \cdot 5 + 2}{5} = \frac{2}{3} x - 4 \frac{1}{2}$

Simplify the numerator.

Multiply $7$ by $5$ .

$\frac{35 + 2}{5} = \frac{2}{3} x - 4 \frac{1}{2}$

Add $35$ and $2$ .

$\frac{37}{5} = \frac{2}{3} x - 4 \frac{1}{2}$

Step 2

Simplify the right side.

Simplify $\frac{2}{3} x - 4 \frac{1}{2}$ .

Convert $4 \frac{1}{2}$ to an improper fraction.

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

$\frac{37}{5} = \frac{2}{3} x - (4 + \frac{1}{2})$

Add $4$ and $\frac{1}{2}$ .

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{37}{5} = \frac{2}{3} x - (4 \cdot \frac{2}{2} + \frac{1}{2})$

Combine $4$ and $\frac{2}{2}$ .

$\frac{37}{5} = \frac{2}{3} x - (\frac{4 \cdot 2}{2} + \frac{1}{2})$

Combine the numerators over the common denominator.

$\frac{37}{5} = \frac{2}{3} x - \frac{4 \cdot 2 + 1}{2}$

Simplify the numerator.

Multiply $4$ by $2$ .

$\frac{37}{5} = \frac{2}{3} x - \frac{8 + 1}{2}$

Add $8$ and $1$ .

$\frac{37}{5} = \frac{2}{3} x - \frac{9}{2}$

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

$\frac{37}{5} = \frac{2 x}{3} - \frac{9}{2}$

Step 3

Rewrite the equation as $\frac{2 x}{3} - \frac{9}{2} = \frac{37}{5}$ .

$\frac{2 x}{3} - \frac{9}{2} = \frac{37}{5}$

Step 4

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

Add $\frac{9}{2}$ to both sides of the equation.

$\frac{2 x}{3} = \frac{37}{5} + \frac{9}{2}$

To write $\frac{37}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2 x}{3} = \frac{37}{5} \cdot \frac{2}{2} + \frac{9}{2}$

To write $\frac{9}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{2 x}{3} = \frac{37}{5} \cdot \frac{2}{2} + \frac{9}{2} \cdot \frac{5}{5}$

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

Multiply $\frac{37}{5}$ by $\frac{2}{2}$ .

$\frac{2 x}{3} = \frac{37 \cdot 2}{5 \cdot 2} + \frac{9}{2} \cdot \frac{5}{5}$

Multiply $5$ by $2$ .

$\frac{2 x}{3} = \frac{37 \cdot 2}{10} + \frac{9}{2} \cdot \frac{5}{5}$

Multiply $\frac{9}{2}$ by $\frac{5}{5}$ .

$\frac{2 x}{3} = \frac{37 \cdot 2}{10} + \frac{9 \cdot 5}{2 \cdot 5}$

Multiply $2$ by $5$ .

$\frac{2 x}{3} = \frac{37 \cdot 2}{10} + \frac{9 \cdot 5}{10}$

Combine the numerators over the common denominator.

$\frac{2 x}{3} = \frac{37 \cdot 2 + 9 \cdot 5}{10}$

Simplify the numerator.

Multiply $37$ by $2$ .

$\frac{2 x}{3} = \frac{74 + 9 \cdot 5}{10}$

Multiply $9$ by $5$ .

$\frac{2 x}{3} = \frac{74 + 45}{10}$

Add $74$ and $45$ .

$\frac{2 x}{3} = \frac{119}{10}$

Step 5

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 x}{3} = \frac{3}{2} \cdot \frac{119}{10}$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{2} \cdot \frac{2 x}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 x}{3} = \frac{3}{2} \cdot \frac{119}{10}$

Rewrite the expression.

$\frac{1}{2} (2 x) = \frac{3}{2} \cdot \frac{119}{10}$

Cancel the common factor of $2$ .

Factor $2$ out of $2 x$ .

$\frac{1}{2} (2 (x)) = \frac{3}{2} \cdot \frac{119}{10}$

Cancel the common factor.

$\frac{1}{2} (2 x) = \frac{3}{2} \cdot \frac{119}{10}$

Rewrite the expression.

$x = \frac{3}{2} \cdot \frac{119}{10}$

Simplify the right side.

Multiply $\frac{3}{2} \cdot \frac{119}{10}$ .

Multiply $\frac{3}{2}$ by $\frac{119}{10}$ .

$x = \frac{3 \cdot 119}{2 \cdot 10}$

Multiply $3$ by $119$ .

$x = \frac{357}{2 \cdot 10}$

Multiply $2$ by $10$ .

$x = \frac{357}{20}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{357}{20}$

Decimal Form:

$x = 17.85$

Mixed Number Form:

$x = 17 \frac{17}{20}$

Solve for x 7 2/5=2/3x-4 1/2

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