Solve for x x/2+(5x)/4=13/4

$\frac{x}{2} + \frac{5 x}{4} = \frac{13}{4}$

Step 1

Simplify $\frac{x}{2} + \frac{5 x}{4}$ .

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

$\frac{x}{2} \cdot \frac{2}{2} + \frac{5 x}{4} = \frac{13}{4}$

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

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

$\frac{x \cdot 2}{2 \cdot 2} + \frac{5 x}{4} = \frac{13}{4}$

Multiply $2$ by $2$ .

$\frac{x \cdot 2}{4} + \frac{5 x}{4} = \frac{13}{4}$

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + 5 x}{4} = \frac{13}{4}$

Simplify the numerator.

Move $2$ to the left of $x$ .

$\frac{2 \cdot x + 5 x}{4} = \frac{13}{4}$

Add $2 x$ and $5 x$ .

$\frac{7 x}{4} = \frac{13}{4}$

Step 2

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

$7 x = 13$

Step 3

Divide each term in $7 x = 13$ by $7$ and simplify.

Divide each term in $7 x = 13$ by $7$ .

$\frac{7 x}{7} = \frac{13}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{13}{7}$

Divide $x$ by $1$ .

$x = \frac{13}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{13}{7}$

Decimal Form:

$x = 1.\overline{857142}$

Mixed Number Form:

$x = 1 \frac{6}{7}$