Algebra Examples

$\frac{1}{2} r - 3 = 3 (4 - \frac{3}{2} r)$

Step 1

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

$\frac{r}{2} - 3 = 3 (4 - \frac{3}{2} r)$

Step 2

Simplify $3 (4 - \frac{3}{2} r)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

$\frac{r}{2} - 3 = 3 (4 - \frac{r \cdot 3}{2})$

Step 2.1.2

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

$\frac{r}{2} - 3 = 3 (4 - \frac{3 r}{2})$

Step 2.2

Simplify by multiplying through.

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Step 2.2.1

Apply the distributive property.

$\frac{r}{2} - 3 = 3 \cdot 4 + 3 (- \frac{3 r}{2})$

Step 2.2.2

Multiply $3$ by $4$ .

$\frac{r}{2} - 3 = 12 + 3 (- \frac{3 r}{2})$

Step 2.3

Multiply $3 (- \frac{3 r}{2})$ .

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Step 2.3.1

Multiply $- 1$ by $3$ .

$\frac{r}{2} - 3 = 12 - 3 \frac{3 r}{2}$

Step 2.3.2

Combine $- 3$ and $\frac{3 r}{2}$ .

$\frac{r}{2} - 3 = 12 + \frac{- 3 (3 r)}{2}$

Step 2.3.3

Multiply $3$ by $- 3$ .

$\frac{r}{2} - 3 = 12 + \frac{- 9 r}{2}$

Step 2.4

Move the negative in front of the fraction.

$\frac{r}{2} - 3 = 12 - \frac{9 r}{2}$

Step 3

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

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Step 3.1

Add $\frac{9 r}{2}$ to both sides of the equation.

$\frac{r}{2} - 3 + \frac{9 r}{2} = 12$

Step 3.2

Combine the numerators over the common denominator.

$- 3 + \frac{r + 9 r}{2} = 12$

Step 3.3

Add $r$ and $9 r$ .

$- 3 + \frac{10 r}{2} = 12$

Step 3.4

Cancel the common factor of $10$ and $2$ .

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Step 3.4.1

Factor $2$ out of $10 r$ .

$- 3 + \frac{2 (5 r)}{2} = 12$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $2$ out of $2$ .

$- 3 + \frac{2 (5 r)}{2 (1)} = 12$

Step 3.4.2.2

Cancel the common factor.

$- 3 + \frac{2 (5 r)}{2 \cdot 1} = 12$

Step 3.4.2.3

Rewrite the expression.

$- 3 + \frac{5 r}{1} = 12$

Step 3.4.2.4

Divide $5 r$ by $1$ .

$- 3 + 5 r = 12$

Step 4

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

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Step 4.1

Add $3$ to both sides of the equation.

$5 r = 12 + 3$

Step 4.2

Add $12$ and $3$ .

$5 r = 15$

Step 5

Divide each term in $5 r = 15$ by $5$ and simplify.

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Step 5.1

Divide each term in $5 r = 15$ by $5$ .

$\frac{5 r}{5} = \frac{15}{5}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $5$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{5 r}{5} = \frac{15}{5}$

Step 5.2.1.2

Divide $r$ by $1$ .

$r = \frac{15}{5}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $15$ by $5$ .

$r = 3$