Solve for r (3a+b)/(2r)=6

$\frac{3 a + b}{2 r} = 6$

Step 1

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$2 r, 1$

The LCM of one and any expression is the expression.

$2 r$

Step 2

Multiply each term in $\frac{3 a + b}{2 r} = 6$ by $2 r$ to eliminate the fractions.

Multiply each term in $\frac{3 a + b}{2 r} = 6$ by $2 r$ .

$\frac{3 a + b}{2 r} (2 r) = 6 (2 r)$

Simplify the left side.

Rewrite using the commutative property of multiplication.

$2 \frac{3 a + b}{2 r} r = 6 (2 r)$

Cancel the common factor of $2$ .

Factor $2$ out of $2 r$ .

$2 \frac{3 a + b}{2 (r)} r = 6 (2 r)$

Cancel the common factor.

$2 \frac{3 a + b}{2 r} r = 6 (2 r)$

Rewrite the expression.

$\frac{3 a + b}{r} r = 6 (2 r)$

Cancel the common factor of $r$ .

Cancel the common factor.

$\frac{3 a + b}{r} r = 6 (2 r)$

Rewrite the expression.

$3 a + b = 6 (2 r)$

Simplify the right side.

Multiply $2$ by $6$ .

$3 a + b = 12 r$

Step 3

Solve the equation.

Rewrite the equation as $12 r = 3 a + b$ .

$12 r = 3 a + b$

Divide each term in $12 r = 3 a + b$ by $12$ and simplify.

Divide each term in $12 r = 3 a + b$ by $12$ .

$\frac{12 r}{12} = \frac{3 a}{12} + \frac{b}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 r}{12} = \frac{3 a}{12} + \frac{b}{12}$

Divide $r$ by $1$ .

$r = \frac{3 a}{12} + \frac{b}{12}$

Simplify the right side.

Cancel the common factor of $3$ and $12$ .

Factor $3$ out of $3 a$ .

$r = \frac{3 (a)}{12} + \frac{b}{12}$

Cancel the common factors.

Factor $3$ out of $12$ .

$r = \frac{3 a}{3 \cdot 4} + \frac{b}{12}$

Cancel the common factor.

$r = \frac{3 a}{3 \cdot 4} + \frac{b}{12}$

Rewrite the expression.

$r = \frac{a}{4} + \frac{b}{12}$

Solve for r (3a+b)/(2r)=6

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