Question

question 22 · 1 point
use cross multiplication to solve the following proportion:
\\(\frac{-6x - 3}{9} = \frac{x + 7}{6}\\).
enter your answer as a reduced fraction if necessary.
provide your answer below:
\\(x = \square\\)

Explanation:

Step1: Apply cross - multiplication

For the proportion \(\frac{-6x - 3}{9}=\frac{x + 7}{6}\), cross - multiplying gives us \(6(-6x - 3)=9(x + 7)\).

Step2: Expand both sides

Expand the left - hand side: \(6\times(-6x)+6\times(-3)=-36x-18\).
Expand the right - hand side: \(9\times x+9\times7 = 9x + 63\).
So the equation becomes \(-36x-18=9x + 63\).

Step3: Move all x terms to one side and constants to the other

Add \(36x\) to both sides: \(-18=9x + 36x+63\), which simplifies to \(-18 = 45x+63\).
Subtract 63 from both sides: \(-18-63=45x\), so \(-81 = 45x\).

Step4: Solve for x

Divide both sides by 45: \(x=\frac{-81}{45}\).
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 9. \(\frac{-81\div9}{45\div9}=\frac{-9}{5}\).

Answer:

\(x =-\frac{9}{5}\)