Simplify 2/3-1/4x+1/2x-1/6

$\frac{2}{3} - \frac{1}{4} x + \frac{1}{2} x - \frac{1}{6}$

Step 1

Simplify each term.

Combine $x$ and $\frac{1}{4}$ .

$\frac{2}{3} - \frac{x}{4} + \frac{1}{2} x - \frac{1}{6}$

Combine $\frac{1}{2}$ and $x$ .

$\frac{2}{3} - \frac{x}{4} + \frac{x}{2} - \frac{1}{6}$

Step 2

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{x}{4} + \frac{x}{2} + \frac{2}{3} \cdot \frac{2}{2} - \frac{1}{6}$

Step 3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{3}$ by $\frac{2}{2}$ .

$- \frac{x}{4} + \frac{x}{2} + \frac{2 \cdot 2}{3 \cdot 2} - \frac{1}{6}$

Multiply $3$ by $2$ .

$- \frac{x}{4} + \frac{x}{2} + \frac{2 \cdot 2}{6} - \frac{1}{6}$

Step 4

Combine the numerators over the common denominator.

$- \frac{x}{4} + \frac{x}{2} + \frac{2 \cdot 2 - 1}{6}$

Step 5

Simplify the numerator.

Multiply $2$ by $2$ .

$- \frac{x}{4} + \frac{x}{2} + \frac{4 - 1}{6}$

Subtract $1$ from $4$ .

$- \frac{x}{4} + \frac{x}{2} + \frac{3}{6}$

Step 6

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3$ .

$- \frac{x}{4} + \frac{x}{2} + \frac{3 (1)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$- \frac{x}{4} + \frac{x}{2} + \frac{3 \cdot 1}{3 \cdot 2}$

Cancel the common factor.

$- \frac{x}{4} + \frac{x}{2} + \frac{3 \cdot 1}{3 \cdot 2}$

Rewrite the expression.

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

Step 7

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

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

Step 8

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

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

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

Multiply $2$ by $2$ .

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

Step 9

Combine the numerators over the common denominator.

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

Step 10

Add $- x$ and $x \cdot 2$ .

Reorder $x$ and $2$ .

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

Add $- x$ and $2 \cdot x$ .

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

Simplify 2/3-1/4x+1/2x-1/6

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