Question

solve for y.
\\(\frac{6}{y - 3} = \frac{4}{3}\\)
simplify your answer as much as possible.

Explanation:

Step1: Cross - multiply

To solve the equation \(\frac{6}{y - 3}=\frac{4}{3}\), we can use cross - multiplication. Cross - multiplication states that if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\). So, applying this to our equation, we get \(6\times3 = 4\times(y - 3)\).
\(18=4(y - 3)\)

Step2: Distribute the 4

We use the distributive property \(a(b + c)=ab+ac\) (in our case \(a = 4\), \(b=y\), \(c=- 3\)) to expand the right - hand side. So, \(4(y - 3)=4y-12\). Our equation becomes:
\(18 = 4y-12\)

Step3: Add 12 to both sides

To isolate the term with \(y\), we add 12 to both sides of the equation.
\(18 + 12=4y-12 + 12\)
\(30 = 4y\)

Step4: Divide both sides by 4

To solve for \(y\), we divide both sides of the equation by 4.
\(y=\frac{30}{4}\)

Step5: Simplify the fraction

We can simplify \(\frac{30}{4}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
\(y=\frac{15}{2}\)

Answer:

\(y = \frac{15}{2}\)