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

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

Step 1

Simplify the left side.

Simplify $5 (x - 3 \frac{3}{4})$ .

Convert $3 \frac{3}{4}$ to an improper fraction.

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

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

Add $3$ and $\frac{3}{4}$ .

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Combine $3$ and $\frac{4}{4}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $4$ .

$5 (x - \frac{12 + 3}{4}) = 7 \frac{1}{2}$

Add $12$ and $3$ .

$5 (x - \frac{15}{4}) = 7 \frac{1}{2}$

Apply the distributive property.

$5 x + 5 (- \frac{15}{4}) = 7 \frac{1}{2}$

Multiply $5 (- \frac{15}{4})$ .

Multiply $- 1$ by $5$ .

$5 x - 5 (\frac{15}{4}) = 7 \frac{1}{2}$

Combine $- 5$ and $\frac{15}{4}$ .

$5 x + \frac{- 5 \cdot 15}{4} = 7 \frac{1}{2}$

Multiply $- 5$ by $15$ .

$5 x + \frac{- 75}{4} = 7 \frac{1}{2}$

Move the negative in front of the fraction.

$5 x - \frac{75}{4} = 7 \frac{1}{2}$

Step 2

Simplify the right side.

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

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

$5 x - \frac{75}{4} = 7 + \frac{1}{2}$

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

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

$5 x - \frac{75}{4} = 7 \cdot \frac{2}{2} + \frac{1}{2}$

Combine $7$ and $\frac{2}{2}$ .

$5 x - \frac{75}{4} = \frac{7 \cdot 2}{2} + \frac{1}{2}$

Combine the numerators over the common denominator.

$5 x - \frac{75}{4} = \frac{7 \cdot 2 + 1}{2}$

Simplify the numerator.

Multiply $7$ by $2$ .

$5 x - \frac{75}{4} = \frac{14 + 1}{2}$

Add $14$ and $1$ .

$5 x - \frac{75}{4} = \frac{15}{2}$

Step 3

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

Add $\frac{75}{4}$ to both sides of the equation.

$5 x = \frac{15}{2} + \frac{75}{4}$

To write $\frac{15}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$5 x = \frac{15}{2} \cdot \frac{2}{2} + \frac{75}{4}$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{15}{2}$ by $\frac{2}{2}$ .

$5 x = \frac{15 \cdot 2}{2 \cdot 2} + \frac{75}{4}$

Multiply $2$ by $2$ .

$5 x = \frac{15 \cdot 2}{4} + \frac{75}{4}$

Combine the numerators over the common denominator.

$5 x = \frac{15 \cdot 2 + 75}{4}$

Simplify the numerator.

Multiply $15$ by $2$ .

$5 x = \frac{30 + 75}{4}$

Add $30$ and $75$ .

$5 x = \frac{105}{4}$

Step 4

Divide each term in $5 x = \frac{105}{4}$ by $5$ and simplify.

Divide each term in $5 x = \frac{105}{4}$ by $5$ .

$\frac{5 x}{5} = \frac{\frac{105}{4}}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{\frac{105}{4}}{5}$

Divide $x$ by $1$ .

$x = \frac{\frac{105}{4}}{5}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{105}{4} \cdot \frac{1}{5}$

Cancel the common factor of $5$ .

Factor $5$ out of $105$ .

$x = \frac{5 (21)}{4} \cdot \frac{1}{5}$

Cancel the common factor.

$x = \frac{5 \cdot 21}{4} \cdot \frac{1}{5}$

Rewrite the expression.

$x = \frac{21}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{21}{4}$

Decimal Form:

$x = 5.25$

Mixed Number Form:

$x = 5 \frac{1}{4}$

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

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