Solve for r -1/2r+3=5/6r+7

$- \frac{1}{2} r + 3 = \frac{5}{6} r + 7$

Step 1

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

$- \frac{r}{2} + 3 = \frac{5}{6} r + 7$

Step 2

Combine $\frac{5}{6}$ and $r$ .

$- \frac{r}{2} + 3 = \frac{5 r}{6} + 7$

Step 3

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

Subtract $\frac{5 r}{6}$ from both sides of the equation.

$- \frac{r}{2} + 3 - \frac{5 r}{6} = 7$

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

$- \frac{r}{2} \cdot \frac{3}{3} - \frac{5 r}{6} + 3 = 7$

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

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

$- \frac{r \cdot 3}{2 \cdot 3} - \frac{5 r}{6} + 3 = 7$

Multiply $2$ by $3$ .

$- \frac{r \cdot 3}{6} - \frac{5 r}{6} + 3 = 7$

Combine the numerators over the common denominator.

$\frac{- r \cdot 3 - 5 r}{6} + 3 = 7$

Simplify each term.

Simplify the numerator.

Factor $r$ out of $- r \cdot 3 - 5 r$ .

Factor $r$ out of $- r \cdot 3$ .

$\frac{r (- 1 \cdot 3) - 5 r}{6} + 3 = 7$

Factor $r$ out of $- 5 r$ .

$\frac{r (- 1 \cdot 3) + r \cdot - 5}{6} + 3 = 7$

Factor $r$ out of $r (- 1 \cdot 3) + r \cdot - 5$ .

$\frac{r (- 1 \cdot 3 - 5)}{6} + 3 = 7$

Multiply $- 1$ by $3$ .

$\frac{r (- 3 - 5)}{6} + 3 = 7$

Subtract $5$ from $- 3$ .

$\frac{r \cdot - 8}{6} + 3 = 7$

Cancel the common factor of $- 8$ and $6$ .

Factor $2$ out of $r \cdot - 8$ .

$\frac{2 (r \cdot - 4)}{6} + 3 = 7$

Cancel the common factors.

Factor $2$ out of $6$ .

$\frac{2 (r \cdot - 4)}{2 (3)} + 3 = 7$

Cancel the common factor.

$\frac{2 (r \cdot - 4)}{2 \cdot 3} + 3 = 7$

Rewrite the expression.

$\frac{r \cdot - 4}{3} + 3 = 7$

Move $- 4$ to the left of $r$ .

$\frac{- 4 \cdot r}{3} + 3 = 7$

Move the negative in front of the fraction.

$- \frac{4 r}{3} + 3 = 7$

Step 4

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

Subtract $3$ from both sides of the equation.

$- \frac{4 r}{3} = 7 - 3$

Subtract $3$ from $7$ .

$- \frac{4 r}{3} = 4$

Step 5

Multiply both sides of the equation by $- \frac{3}{4}$ .

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

Step 6

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

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

Move the leading negative in $- \frac{4 r}{3}$ into the numerator.

$\frac{- 3}{4} \cdot \frac{- 4 r}{3} = - \frac{3}{4} \cdot 4$

Factor $3$ out of $- 3$ .

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

Cancel the common factor.

$\frac{3 \cdot - 1}{4} \cdot \frac{- 4 r}{3} = - \frac{3}{4} \cdot 4$

Rewrite the expression.

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

Cancel the common factor of $4$ .

Factor $4$ out of $- 4 r$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- - r = - \frac{3}{4} \cdot 4$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 r = - \frac{3}{4} \cdot 4$

Multiply $r$ by $1$ .

$r = - \frac{3}{4} \cdot 4$

Simplify the right side.

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$r = \frac{- 3}{4} \cdot 4$

Cancel the common factor.

$r = \frac{- 3}{4} \cdot 4$

Rewrite the expression.

$r = - 3$

Solve for r -1/2r+3=5/6r+7

Related Questions

Support LCMGCF.com by disabling your adblocker.