Question

solve the equation. 4(3y - 1) - 3(2y) = 10 y = (type an integer or a simplified fraction.)

Explanation:

Step1: Expand the brackets

First, we expand the terms in the equation \(4(3y - 1)-3(2y)=10\). Using the distributive property \(a(b + c)=ab+ac\), we get:
\(4\times3y-4\times1 - 3\times2y=10\)
\(12y-4 - 6y=10\)

Step2: Combine like terms

Next, we combine the like terms (the terms with \(y\)). \(12y-6y = 6y\), so the equation becomes:
\(6y-4=10\)

Step3: Isolate the variable term

Then, we add 4 to both sides of the equation to isolate the term with \(y\).
\(6y-4 + 4=10 + 4\)
\(6y=14\)

Step4: Solve for y

Finally, we divide both sides by 6 to solve for \(y\).
\(y=\frac{14}{6}\)
Simplifying the fraction \(\frac{14}{6}\) by dividing both the numerator and the denominator by 2, we get \(y = \frac{7}{3}\)

Answer:

\(\frac{7}{3}\)