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Math  /  Algebra

QuestionSolve the proportion. (Simplify your answer completely.) x=□−9x=69x=\square \frac{-9}{x}=\frac{6}{9} Need Help? Read It

Studdy Solution

STEP 1

1. The problem involves solving a proportion between two fractions.
2. The proportion is given by −9x=69\frac{-9}{x} = \frac{6}{9}.
3. The solution requires finding the value of xx that satisfies this equation.
4. The final answer should be simplified completely.

STEP 2

1. Set up the proportion equation.
2. Cross-multiply to eliminate the fractions.
3. Solve the resulting equation for xx.
4. Simplify the solution.

STEP 3

Set up the proportion equation:
−9x=69\frac{-9}{x} = \frac{6}{9}

STEP 4

Cross-multiply to eliminate the fractions:
−9⋅9=6⋅x-9 \cdot 9 = 6 \cdot x

STEP 5

Simplify the equation obtained from cross-multiplication:
−81=6x-81 = 6x

STEP 6

Solve for xx by dividing both sides of the equation by 6:
x=−816x = \frac{-81}{6}

STEP 7

Simplify the fraction:
x=−816=−27⋅32⋅3=−272x = \frac{-81}{6} = \frac{-27 \cdot 3}{2 \cdot 3} = \frac{-27}{2}
So, the simplified answer is:
x=−272x = -\frac{27}{2}
Solution: x=−272x = -\frac{27}{2}

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