Question

solve the equation.
3(2y - 1) - 2(2y) = 2

y = \square
(type an integer or a simplified fraction.)

Explanation:

Step1: Expand the brackets

First, we use the distributive property (also known as the distributive law) to expand the terms in the equation. The distributive property states that \(a(b + c)=ab+ac\) and \(a(b - c)=ab - ac\).

For \(3(2y - 1)\), we multiply 3 by each term inside the brackets: \(3\times2y-3\times1 = 6y-3\).

For \(-2(2y)\), we multiply -2 by 2y: \(- 2\times2y=-4y\).

So the equation becomes: \(6y - 3-4y=2\).

Step2: Combine like terms

Next, we combine the like terms (terms with the same variable \(y\)). The terms \(6y\) and \(-4y\) are like terms.

\(6y-4y=(6 - 4)y = 2y\).

So the equation simplifies to: \(2y-3 = 2\).

Step3: Isolate the variable term

We want to isolate the term with \(y\) on one side of the equation. To do this, we add 3 to both sides of the equation (using the addition property of equality, which states that if \(a=b\), then \(a + c=b + c\)).

Adding 3 to both sides: \(2y-3 + 3=2 + 3\).

Simplifying both sides: \(2y=5\).

Step4: Solve for y

To solve for \(y\), we divide both sides of the equation by 2 (using the division property of equality, which states that if \(a=b\) and \(c
eq0\), then \(\frac{a}{c}=\frac{b}{c}\)).

Dividing both sides by 2: \(\frac{2y}{2}=\frac{5}{2}\).

Simplifying: \(y=\frac{5}{2}\).

Answer:

\(\frac{5}{2}\)