Solve for x 3/4(x+21)=10 1/2

$\frac{3}{4} (x + 21) = 10 \frac{1}{2}$

Step 1

Simplify the left side.

Simplify $\frac{3}{4} \cdot (x + 21)$ .

Apply the distributive property.

$\frac{3}{4} x + \frac{3}{4} \cdot 21 = 10 \frac{1}{2}$

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

$\frac{3 x}{4} + \frac{3}{4} \cdot 21 = 10 \frac{1}{2}$

Multiply $\frac{3}{4} \cdot 21$ .

Combine $\frac{3}{4}$ and $21$ .

$\frac{3 x}{4} + \frac{3 \cdot 21}{4} = 10 \frac{1}{2}$

Multiply $3$ by $21$ .

$\frac{3 x}{4} + \frac{63}{4} = 10 \frac{1}{2}$

Step 2

Simplify the right side.

Convert $10 \frac{1}{2}$ to an improper fraction.

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

$\frac{3 x}{4} + \frac{63}{4} = 10 + \frac{1}{2}$

Add $10$ and $\frac{1}{2}$ .

To write $10$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x}{4} + \frac{63}{4} = 10 \cdot \frac{2}{2} + \frac{1}{2}$

Combine $10$ and $\frac{2}{2}$ .

$\frac{3 x}{4} + \frac{63}{4} = \frac{10 \cdot 2}{2} + \frac{1}{2}$

Combine the numerators over the common denominator.

$\frac{3 x}{4} + \frac{63}{4} = \frac{10 \cdot 2 + 1}{2}$

Simplify the numerator.

Multiply $10$ by $2$ .

$\frac{3 x}{4} + \frac{63}{4} = \frac{20 + 1}{2}$

Add $20$ and $1$ .

$\frac{3 x}{4} + \frac{63}{4} = \frac{21}{2}$

Step 3

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

Subtract $\frac{63}{4}$ from both sides of the equation.

$\frac{3 x}{4} = \frac{21}{2} - \frac{63}{4}$

To write $\frac{21}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x}{4} = \frac{21}{2} \cdot \frac{2}{2} - \frac{63}{4}$

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

Multiply $\frac{21}{2}$ by $\frac{2}{2}$ .

$\frac{3 x}{4} = \frac{21 \cdot 2}{2 \cdot 2} - \frac{63}{4}$

Multiply $2$ by $2$ .

$\frac{3 x}{4} = \frac{21 \cdot 2}{4} - \frac{63}{4}$

Combine the numerators over the common denominator.

$\frac{3 x}{4} = \frac{21 \cdot 2 - 63}{4}$

Simplify the numerator.

Multiply $21$ by $2$ .

$\frac{3 x}{4} = \frac{42 - 63}{4}$

Subtract $63$ from $42$ .

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

Move the negative in front of the fraction.

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

Step 4

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

$3 x = - 21$

Step 5

Divide each term in $3 x = - 21$ by $3$ and simplify.

Divide each term in $3 x = - 21$ by $3$ .

$\frac{3 x}{3} = \frac{- 21}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 21}{3}$

Divide $x$ by $1$ .

$x = \frac{- 21}{3}$

Simplify the right side.

Divide $- 21$ by $3$ .

$x = - 7$

Solve for x 3/4(x+21)=10 1/2

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