Solve for s -27/5s+7/3=41/6

$- \frac{27}{5} s + \frac{7}{3} = \frac{41}{6}$

Simplify each term.

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Combine $s$ and $\frac{27}{5}$ .

$- \frac{s \cdot 27}{5} + \frac{7}{3} = \frac{41}{6}$

Move $27$ to the left of $s$ .

$- \frac{27 s}{5} + \frac{7}{3} = \frac{41}{6}$

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

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Subtract $\frac{7}{3}$ from both sides of the equation.

$- \frac{27 s}{5} = \frac{41}{6} - \frac{7}{3}$

To write $- \frac{7}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{27 s}{5} = \frac{41}{6} - \frac{7}{3} \cdot \frac{2}{2}$

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

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Multiply $\frac{7}{3}$ and $\frac{2}{2}$ .

$- \frac{27 s}{5} = \frac{41}{6} - \frac{7 \cdot 2}{3 \cdot 2}$

Multiply $3$ by $2$ .

$- \frac{27 s}{5} = \frac{41}{6} - \frac{7 \cdot 2}{6}$

Combine the numerators over the common denominator.

$- \frac{27 s}{5} = \frac{41 - 7 \cdot 2}{6}$

Simplify the numerator.

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Multiply $- 7$ by $2$ .

$- \frac{27 s}{5} = \frac{41 - 14}{6}$

Subtract $14$ from $41$ .

$- \frac{27 s}{5} = \frac{27}{6}$

Cancel the common factor of $27$ and $6$ .

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Factor $3$ out of $27$ .

$- \frac{27 s}{5} = \frac{3 (9)}{6}$

Cancel the common factors.

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Factor $3$ out of $6$ .

$- \frac{27 s}{5} = \frac{3 \cdot 9}{3 \cdot 2}$

Cancel the common factor.

$- \frac{27 s}{5} = \frac{3 \cdot 9}{3 \cdot 2}$

Rewrite the expression.

$- \frac{27 s}{5} = \frac{9}{2}$

Multiply both sides of the equation by $- \frac{5}{27}$ .

$- \frac{5}{27} \cdot (- \frac{27 s}{5}) = - \frac{5}{27} \cdot \frac{9}{2}$

Simplify both sides of the equation.

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Simplify $- \frac{5}{27} \cdot (- \frac{27 s}{5})$ .

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Cancel the common factor of $5$ .

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Move the leading negative in $- \frac{5}{27}$ into the numerator.

$\frac{- 5}{27} \cdot (- \frac{27 s}{5}) = - \frac{5}{27} \cdot \frac{9}{2}$

Move the leading negative in $- \frac{27 s}{5}$ into the numerator.

$\frac{- 5}{27} \cdot \frac{- 27 s}{5} = - \frac{5}{27} \cdot \frac{9}{2}$

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{27} \cdot \frac{- 27 s}{5} = - \frac{5}{27} \cdot \frac{9}{2}$

Cancel the common factor.

$\frac{5 \cdot - 1}{27} \cdot \frac{- 27 s}{5} = - \frac{5}{27} \cdot \frac{9}{2}$

Rewrite the expression.

$\frac{- 1}{27} \cdot (- 27 s) = - \frac{5}{27} \cdot \frac{9}{2}$

Cancel the common factor of $27$ .

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Factor $27$ out of $- 27 s$ .

$\frac{- 1}{27} \cdot (27 (- s)) = - \frac{5}{27} \cdot \frac{9}{2}$

Cancel the common factor.

$\frac{- 1}{27} \cdot (27 (- s)) = - \frac{5}{27} \cdot \frac{9}{2}$

Rewrite the expression.

$- 1 \cdot (- s) = - \frac{5}{27} \cdot \frac{9}{2}$

Multiply.

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Multiply $- 1$ by $- 1$ .

$1 \cdot s = - \frac{5}{27} \cdot \frac{9}{2}$

Multiply $s$ by $1$ .

$s = - \frac{5}{27} \cdot \frac{9}{2}$

Simplify $- \frac{5}{27} \cdot \frac{9}{2}$ .

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Cancel the common factor of $9$ .

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Move the leading negative in $- \frac{5}{27}$ into the numerator.

$s = \frac{- 5}{27} \cdot \frac{9}{2}$

Factor $9$ out of $27$ .

$s = \frac{- 5}{9 (3)} \cdot \frac{9}{2}$

Cancel the common factor.

$s = \frac{- 5}{9 \cdot 3} \cdot \frac{9}{2}$

Rewrite the expression.

$s = \frac{- 5}{3} \cdot \frac{1}{2}$

Multiply $\frac{- 5}{3}$ and $\frac{1}{2}$ .

$s = \frac{- 5}{3 \cdot 2}$

Simplify the expression.

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Multiply $3$ by $2$ .

$s = \frac{- 5}{6}$

Move the negative in front of the fraction.

$s = - \frac{5}{6}$

The result can be shown in multiple forms.

Exact Form:

$s = - \frac{5}{6}$

Decimal Form:

$s = - 0.8\overline{3}$

Solve for s -27/5s+7/3=41/6

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