Solve for r 7-5/2(8r-6)+2r=32

$7 - \frac{5}{2} (8 r - 6) + 2 r = 32$

Simplify $7 - \frac{5}{2} \cdot (8 r - 6) + 2 r$ .

Simplify each term.

Apply the distributive property.

$7 - \frac{5}{2} (8 r) - \frac{5}{2} \cdot - 6 + 2 r = 32$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$7 + \frac{- 5}{2} (8 r) - \frac{5}{2} \cdot - 6 + 2 r = 32$

Factor $2$ out of $8 r$ .

$7 + \frac{- 5}{2} (2 (4 r)) - \frac{5}{2} \cdot - 6 + 2 r = 32$

Cancel the common factor.

$7 + \frac{- 5}{2} (2 (4 r)) - \frac{5}{2} \cdot - 6 + 2 r = 32$

Rewrite the expression.

$7 - 5 (4 r) - \frac{5}{2} \cdot - 6 + 2 r = 32$

Multiply $4$ by $- 5$ .

$7 - 20 r - \frac{5}{2} \cdot - 6 + 2 r = 32$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$7 - 20 r + \frac{- 5}{2} \cdot - 6 + 2 r = 32$

Factor $2$ out of $- 6$ .

$7 - 20 r + \frac{- 5}{2} \cdot (2 (- 3)) + 2 r = 32$

Cancel the common factor.

$7 - 20 r + \frac{- 5}{2} \cdot (2 \cdot - 3) + 2 r = 32$

Rewrite the expression.

$7 - 20 r - 5 \cdot - 3 + 2 r = 32$

Multiply $- 5$ by $- 3$ .

$7 - 20 r + 15 + 2 r = 32$

Simplify by adding terms.

Add $7$ and $15$ .

$- 20 r + 22 + 2 r = 32$

Add $- 20 r$ and $2 r$ .

$- 18 r + 22 = 32$

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

Subtract $22$ from both sides of the equation.

$- 18 r = 32 - 22$

Subtract $22$ from $32$ .

$- 18 r = 10$

Divide each term in $- 18 r = 10$ by $- 18$ and simplify.

Divide each term in $- 18 r = 10$ by $- 18$ .

$\frac{- 18 r}{- 18} = \frac{10}{- 18}$

Simplify the left side.

Cancel the common factor of $- 18$ .

Cancel the common factor.

$\frac{- 18 r}{- 18} = \frac{10}{- 18}$

Divide $r$ by $1$ .

$r = \frac{10}{- 18}$

Simplify the right side.

Cancel the common factor of $10$ and $- 18$ .

Factor $2$ out of $10$ .

$r = \frac{2 (5)}{- 18}$

Cancel the common factors.

Factor $2$ out of $- 18$ .

$r = \frac{2 \cdot 5}{2 \cdot - 9}$

Cancel the common factor.

$r = \frac{2 \cdot 5}{2 \cdot - 9}$

Rewrite the expression.

$r = \frac{5}{- 9}$

Move the negative in front of the fraction.

$r = - \frac{5}{9}$

The result can be shown in multiple forms.

Exact Form:

$r = - \frac{5}{9}$

Decimal Form:

$r = - 0.\overline{5}$

Solve for r 7-5/2(8r-6)+2r=32

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