Solve for x x-1/2=1 1/4

$x - \frac{1}{2} = 1 \frac{1}{4}$

Step 1

Simplify the right side.

Convert $1 \frac{1}{4}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$x - \frac{1}{2} = 1 + \frac{1}{4}$

Add $1$ and $\frac{1}{4}$ .

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

$x - \frac{1}{2} = \frac{4}{4} + \frac{1}{4}$

Combine the numerators over the common denominator.

$x - \frac{1}{2} = \frac{4 + 1}{4}$

Add $4$ and $1$ .

$x - \frac{1}{2} = \frac{5}{4}$

Step 2

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

Add $\frac{1}{2}$ to both sides of the equation.

$x = \frac{5}{4} + \frac{1}{2}$

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = \frac{5}{4} + \frac{1}{2} \cdot \frac{2}{2}$

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

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

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

Multiply $2$ by $2$ .

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

Combine the numerators over the common denominator.

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

Add $5$ and $2$ .

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.75$

Mixed Number Form:

$x = 1 \frac{3}{4}$