Solve for x 8/5x-4=x+4/5

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

Step 1

Combine $\frac{8}{5}$ and $x$ .

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

Step 2

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

Subtract $x$ from both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $8 x - x \cdot 5$ .

Factor $x$ out of $8 x$ .

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

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

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

Factor $x$ out of $x \cdot 8 + x (- 1 \cdot 5)$ .

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

Multiply $- 1$ by $5$ .

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

Subtract $5$ from $8$ .

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

Move $3$ to the left of $x$ .

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

Step 3

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

Add $4$ to both sides of the equation.

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

To write $4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $4$ by $5$ .

$\frac{3 x}{5} = \frac{4 + 20}{5}$

Add $4$ and $20$ .

$\frac{3 x}{5} = \frac{24}{5}$

Step 4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$3 x = 24$

Step 5

Divide each term in $3 x = 24$ by $3$ and simplify.

Divide each term in $3 x = 24$ by $3$ .

$\frac{3 x}{3} = \frac{24}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{24}{3}$

Divide $x$ by $1$ .

$x = \frac{24}{3}$

Simplify the right side.

Divide $24$ by $3$ .

$x = 8$

Solve for x 8/5x-4=x+4/5

Related Questions

Support LCMGCF.com by disabling your adblocker.