Question

problems 9–10: spiral review
solve each equation.
use paper or the sketch tool if it helps with your thinking.
\\(\frac{3y - 6}{9} = \frac{4 - 2y}{-3}\\)
\\(0.3(x - 10) - 1.8 = 2.7x\\)

Explanation:

Step1: Cross - multiply the equation

Given the equation \(\frac{3y - 6}{9}=\frac{4 - 2y}{-3}\), cross - multiplying (which is based on the property that if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\)) gives us \((3y - 6)\times(- 3)=9\times(4 - 2y)\).

Step2: Expand both sides

Expanding the left - hand side: \((3y-6)\times(-3)=3y\times(-3)-6\times(-3)=-9y + 18\)
Expanding the right - hand side: \(9\times(4 - 2y)=9\times4-9\times2y = 36-18y\)
So the equation becomes \(-9y + 18=36-18y\).

Step3: Move the terms with y to one side

Add \(18y\) to both sides of the equation: \(-9y+18y + 18=36-18y + 18y\)
Simplifying, we get \(9y+18 = 36\).

Step4: Solve for y

Subtract 18 from both sides: \(9y+18 - 18=36 - 18\)
Which simplifies to \(9y=18\).
Divide both sides by 9: \(y=\frac{18}{9}=2\).

Answer:

\(y = 2\)