Solve for f 3/4f=2+1/2f-7/8-f

$\frac{3}{4} f = 2 + \frac{1}{2} f - \frac{7}{8} - f$

Step 1

Since $f$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$2 + \frac{1}{2} f - \frac{7}{8} - f = \frac{3}{4} f$

Step 2

Simplify $2 + \frac{1}{2} f - \frac{7}{8} - f$ .

Combine $\frac{1}{2}$ and $f$ .

$2 + \frac{f}{2} - \frac{7}{8} - f = \frac{3}{4} f$

To write $2$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{f}{2} + 2 \cdot \frac{8}{8} - \frac{7}{8} - f = \frac{3}{4} f$

Combine $2$ and $\frac{8}{8}$ .

$\frac{f}{2} + \frac{2 \cdot 8}{8} - \frac{7}{8} - f = \frac{3}{4} f$

Combine the numerators over the common denominator.

$\frac{f}{2} + \frac{2 \cdot 8 - 7}{8} - f = \frac{3}{4} f$

Simplify the numerator.

Multiply $2$ by $8$ .

$\frac{f}{2} + \frac{16 - 7}{8} - f = \frac{3}{4} f$

Subtract $7$ from $16$ .

$\frac{f}{2} + \frac{9}{8} - f = \frac{3}{4} f$

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

$\frac{f}{2} - f \cdot \frac{2}{2} + \frac{9}{8} = \frac{3}{4} f$

Simplify terms.

Combine $- f$ and $\frac{2}{2}$ .

$\frac{f}{2} + \frac{- f \cdot 2}{2} + \frac{9}{8} = \frac{3}{4} f$

Combine the numerators over the common denominator.

$\frac{f - f \cdot 2}{2} + \frac{9}{8} = \frac{3}{4} f$

Simplify each term.

Simplify the numerator.

Factor $f$ out of $f - f \cdot 2$ .

Raise $f$ to the power of $1$ .

$\frac{f^{1} - f \cdot 2}{2} + \frac{9}{8} = \frac{3}{4} f$

Factor $f$ out of $f^{1}$ .

$\frac{f \cdot 1 - f \cdot 2}{2} + \frac{9}{8} = \frac{3}{4} f$

Factor $f$ out of $- f \cdot 2$ .

$\frac{f \cdot 1 + f (- 1 \cdot 2)}{2} + \frac{9}{8} = \frac{3}{4} f$

Factor $f$ out of $f \cdot 1 + f (- 1 \cdot 2)$ .

$\frac{f (1 - 1 \cdot 2)}{2} + \frac{9}{8} = \frac{3}{4} f$

Multiply $- 1$ by $2$ .

$\frac{f (1 - 2)}{2} + \frac{9}{8} = \frac{3}{4} f$

Subtract $2$ from $1$ .

$\frac{f \cdot - 1}{2} + \frac{9}{8} = \frac{3}{4} f$

Move $- 1$ to the left of $f$ .

$\frac{- 1 \cdot f}{2} + \frac{9}{8} = \frac{3}{4} f$

Move the negative in front of the fraction.

$- \frac{f}{2} + \frac{9}{8} = \frac{3}{4} f$

Step 3

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

$- \frac{f}{2} + \frac{9}{8} = \frac{3 f}{4}$

Step 4

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

Subtract $\frac{3 f}{4}$ from both sides of the equation.

$- \frac{f}{2} + \frac{9}{8} - \frac{3 f}{4} = 0$

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

$- \frac{f}{2} \cdot \frac{2}{2} - \frac{3 f}{4} + \frac{9}{8} = 0$

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

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

$- \frac{f \cdot 2}{2 \cdot 2} - \frac{3 f}{4} + \frac{9}{8} = 0$

Multiply $2$ by $2$ .

$- \frac{f \cdot 2}{4} - \frac{3 f}{4} + \frac{9}{8} = 0$

Combine the numerators over the common denominator.

$\frac{- f \cdot 2 - 3 f}{4} + \frac{9}{8} = 0$

Simplify each term.

Simplify the numerator.

Factor $f$ out of $- f \cdot 2 - 3 f$ .

Factor $f$ out of $- f \cdot 2$ .

$\frac{f (- 1 \cdot 2) - 3 f}{4} + \frac{9}{8} = 0$

Factor $f$ out of $- 3 f$ .

$\frac{f (- 1 \cdot 2) + f \cdot - 3}{4} + \frac{9}{8} = 0$

Factor $f$ out of $f (- 1 \cdot 2) + f \cdot - 3$ .

$\frac{f (- 1 \cdot 2 - 3)}{4} + \frac{9}{8} = 0$

Multiply $- 1$ by $2$ .

$\frac{f (- 2 - 3)}{4} + \frac{9}{8} = 0$

Subtract $3$ from $- 2$ .

$\frac{f \cdot - 5}{4} + \frac{9}{8} = 0$

Move $- 5$ to the left of $f$ .

$\frac{- 5 \cdot f}{4} + \frac{9}{8} = 0$

Move the negative in front of the fraction.

$- \frac{5 f}{4} + \frac{9}{8} = 0$

Step 5

Subtract $\frac{9}{8}$ from both sides of the equation.

$- \frac{5 f}{4} = - \frac{9}{8}$

Step 6

Multiply both sides of the equation by $- \frac{4}{5}$ .

$- \frac{4}{5} (- \frac{5 f}{4}) = - \frac{4}{5} (- \frac{9}{8})$

Step 7

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{5}$ into the numerator.

$\frac{- 4}{5} (- \frac{5 f}{4}) = - \frac{4}{5} (- \frac{9}{8})$

Move the leading negative in $- \frac{5 f}{4}$ into the numerator.

$\frac{- 4}{5} \cdot \frac{- 5 f}{4} = - \frac{4}{5} (- \frac{9}{8})$

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{5} \cdot \frac{- 5 f}{4} = - \frac{4}{5} (- \frac{9}{8})$

Cancel the common factor.

$\frac{4 \cdot - 1}{5} \cdot \frac{- 5 f}{4} = - \frac{4}{5} (- \frac{9}{8})$

Rewrite the expression.

$\frac{- 1}{5} (- 5 f) = - \frac{4}{5} (- \frac{9}{8})$

Cancel the common factor of $5$ .

Factor $5$ out of $- 5 f$ .

$\frac{- 1}{5} (5 (- f)) = - \frac{4}{5} (- \frac{9}{8})$

Cancel the common factor.

$\frac{- 1}{5} (5 (- f)) = - \frac{4}{5} (- \frac{9}{8})$

Rewrite the expression.

$- - f = - \frac{4}{5} (- \frac{9}{8})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 f = - \frac{4}{5} (- \frac{9}{8})$

Multiply $f$ by $1$ .

$f = - \frac{4}{5} (- \frac{9}{8})$

Simplify the right side.

Simplify $- \frac{4}{5} (- \frac{9}{8})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{5}$ into the numerator.

$f = \frac{- 4}{5} (- \frac{9}{8})$

Move the leading negative in $- \frac{9}{8}$ into the numerator.

$f = \frac{- 4}{5} \cdot \frac{- 9}{8}$

Factor $4$ out of $- 4$ .

$f = \frac{4 (- 1)}{5} \cdot \frac{- 9}{8}$

Factor $4$ out of $8$ .

$f = \frac{4 \cdot - 1}{5} \cdot \frac{- 9}{4 \cdot 2}$

Cancel the common factor.

$f = \frac{4 \cdot - 1}{5} \cdot \frac{- 9}{4 \cdot 2}$

Rewrite the expression.

$f = \frac{- 1}{5} \cdot \frac{- 9}{2}$

Multiply $\frac{- 1}{5}$ by $\frac{- 9}{2}$ .

$f = \frac{- - 9}{5 \cdot 2}$

Multiply.

Multiply $- 1$ by $- 9$ .

$f = \frac{9}{5 \cdot 2}$

Multiply $5$ by $2$ .

$f = \frac{9}{10}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$f = \frac{9}{10}$

Decimal Form:

$f = 0.9$

Solve for f 3/4f=2+1/2f-7/8-f

Related Questions

Support LCMGCF.com by disabling your adblocker.