Solve for x 3/4x-21=6-1 1/2x

$\frac{3}{4} x - 21 = 6 - 1 \frac{1}{2} x$

Simplify the left side.

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

$\frac{3 x}{4} - 21 = 6 - 1 \frac{1}{2} x$

Simplify the right side.

Simplify $6 - 1 \frac{1}{2} x$ .

Convert $1 \frac{1}{2}$ to an improper fraction.

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

$\frac{3 x}{4} - 21 = 6 - (1 + \frac{1}{2}) x$

Add $1$ and $\frac{1}{2}$ .

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

$\frac{3 x}{4} - 21 = 6 - (\frac{2}{2} + \frac{1}{2}) x$

Combine the numerators over the common denominator.

$\frac{3 x}{4} - 21 = 6 - \frac{2 + 1}{2} x$

Add $2$ and $1$ .

$\frac{3 x}{4} - 21 = 6 - \frac{3}{2} x$

Simplify each term.

Combine $x$ and $\frac{3}{2}$ .

$\frac{3 x}{4} - 21 = 6 - \frac{x \cdot 3}{2}$

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

$\frac{3 x}{4} - 21 = 6 - \frac{3 x}{2}$

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

Add $\frac{3 x}{2}$ to both sides of the equation.

$\frac{3 x}{4} - 21 + \frac{3 x}{2} = 6$

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

$\frac{3 x}{4} + \frac{3 x}{2} \cdot \frac{2}{2} - 21 = 6$

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

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

$\frac{3 x}{4} + \frac{3 x \cdot 2}{2 \cdot 2} - 21 = 6$

Multiply $2$ by $2$ .

$\frac{3 x}{4} + \frac{3 x \cdot 2}{4} - 21 = 6$

Combine the numerators over the common denominator.

$\frac{3 x + 3 x \cdot 2}{4} - 21 = 6$

Simplify the numerator.

Factor $3 x$ out of $3 x + 3 x \cdot 2$ .

Factor $3 x$ out of $3 x$ .

$\frac{3 x (1) + 3 x \cdot 2}{4} - 21 = 6$

Factor $3 x$ out of $3 x \cdot 2$ .

$\frac{3 x (1) + 3 x (2)}{4} - 21 = 6$

Factor $3 x$ out of $3 x (1) + 3 x (2)$ .

$\frac{3 x (1 + 2)}{4} - 21 = 6$

Add $1$ and $2$ .

$\frac{3 x \cdot 3}{4} - 21 = 6$

Multiply $3$ by $3$ .

$\frac{9 x}{4} - 21 = 6$

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

Add $21$ to both sides of the equation.

$\frac{9 x}{4} = 6 + 21$

Add $6$ and $21$ .

$\frac{9 x}{4} = 27$

Multiply both sides of the equation by $\frac{4}{9}$ .

$\frac{4}{9} \cdot \frac{9 x}{4} = \frac{4}{9} \cdot 27$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{9} \cdot \frac{9 x}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{9} \cdot \frac{9 x}{4} = \frac{4}{9} \cdot 27$

Rewrite the expression.

$\frac{1}{9} (9 x) = \frac{4}{9} \cdot 27$

Cancel the common factor of $9$ .

Factor $9$ out of $9 x$ .

$\frac{1}{9} (9 (x)) = \frac{4}{9} \cdot 27$

Cancel the common factor.

$\frac{1}{9} (9 x) = \frac{4}{9} \cdot 27$

Rewrite the expression.

$x = \frac{4}{9} \cdot 27$

Simplify the right side.

Simplify $\frac{4}{9} \cdot 27$ .

Cancel the common factor of $9$ .

Factor $9$ out of $27$ .

$x = \frac{4}{9} \cdot (9 (3))$

Cancel the common factor.

$x = \frac{4}{9} \cdot (9 \cdot 3)$

Rewrite the expression.

$x = 4 \cdot 3$

Multiply $4$ by $3$ .

$x = 12$

Solve for x 3/4x-21=6-1 1/2x

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