Solve for x x+5/4=3/4x

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

Step 1

Simplify $\frac{3}{4} x$ .

Rewrite.

$x + \frac{5}{4} = 0 + 0 + \frac{3}{4} x$

Simplify by adding zeros.

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

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

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

Step 2

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

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

$x + \frac{5}{4} - \frac{3 x}{4} = 0$

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

$x \cdot \frac{4}{4} - \frac{3 x}{4} + \frac{5}{4} = 0$

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

$\frac{x \cdot 4}{4} - \frac{3 x}{4} + \frac{5}{4} = 0$

Combine the numerators over the common denominator.

$\frac{x \cdot 4 - 3 x}{4} + \frac{5}{4} = 0$

Combine the numerators over the common denominator.

$\frac{x \cdot 4 - 3 x + 5}{4} = 0$

Move $4$ to the left of $x$ .

$\frac{4 x - 3 x + 5}{4} = 0$

Subtract $3 x$ from $4 x$ .

$\frac{x + 5}{4} = 0$

Step 3

Set the numerator equal to zero.

$x + 5 = 0$

Step 4

Subtract $5$ from both sides of the equation.

$x = - 5$