Solve for x 1=4/5-(x-4/5)+5/4x

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

Step 1

Rewrite the equation as $\frac{4}{5} - (x - \frac{4}{5}) + \frac{5}{4} x = 1$ .

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

Step 2

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

Simplify each term.

Apply the distributive property.

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

Multiply $- - \frac{4}{5}$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $\frac{4}{5}$ by $1$ .

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

Combine $\frac{5}{4}$ and $x$ .

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

Combine fractions.

Combine the numerators over the common denominator.

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

Add $4$ and $4$ .

$- x + \frac{8}{5} + \frac{5 x}{4} = 1$

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

$- x \cdot \frac{4}{4} + \frac{5 x}{4} + \frac{8}{5} = 1$

Simplify terms.

Combine $- x$ and $\frac{4}{4}$ .

$\frac{- x \cdot 4}{4} + \frac{5 x}{4} + \frac{8}{5} = 1$

Combine the numerators over the common denominator.

$\frac{- x \cdot 4 + 5 x}{4} + \frac{8}{5} = 1$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- x \cdot 4 + 5 x$ .

Factor $x$ out of $- x \cdot 4$ .

$\frac{x (- 1 \cdot 4) + 5 x}{4} + \frac{8}{5} = 1$

Factor $x$ out of $5 x$ .

$\frac{x (- 1 \cdot 4) + x \cdot 5}{4} + \frac{8}{5} = 1$

Factor $x$ out of $x (- 1 \cdot 4) + x \cdot 5$ .

$\frac{x (- 1 \cdot 4 + 5)}{4} + \frac{8}{5} = 1$

Multiply $- 1$ by $4$ .

$\frac{x (- 4 + 5)}{4} + \frac{8}{5} = 1$

Add $- 4$ and $5$ .

$\frac{x \cdot 1}{4} + \frac{8}{5} = 1$

Multiply $x$ by $1$ .

$\frac{x}{4} + \frac{8}{5} = 1$

Step 3

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

Subtract $\frac{8}{5}$ from both sides of the equation.

$\frac{x}{4} = 1 - \frac{8}{5}$

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

$\frac{x}{4} = \frac{5}{5} - \frac{8}{5}$

Combine the numerators over the common denominator.

$\frac{x}{4} = \frac{5 - 8}{5}$

Subtract $8$ from $5$ .

$\frac{x}{4} = \frac{- 3}{5}$

Move the negative in front of the fraction.

$\frac{x}{4} = - \frac{3}{5}$

Step 4

Multiply both sides of the equation by $4$ .

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

Step 5

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

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

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

Multiply $- 1$ by $4$ .

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

Combine $- 4$ and $\frac{3}{5}$ .

$x = \frac{- 4 \cdot 3}{5}$

Multiply $- 4$ by $3$ .

$x = \frac{- 12}{5}$

Move the negative in front of the fraction.

$x = - \frac{12}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{12}{5}$

Decimal Form:

$x = - 2.4$

Mixed Number Form:

$x = - 2 \frac{2}{5}$

Solve for x 1=4/5-(x-4/5)+5/4x

Related Questions

Support LCMGCF.com by disabling your adblocker.