Problem 190 Solve for the formula for \(y\).... [FREE SOLUTION]

Chapter 2: Problem 190

Solve for the formula for \(y\). Solve the formula \(3 x+2 y=11\) for \(y\).

Short Answer

Expert verified

y = \frac{11 - 3x}{2}

Step by step solution

- Isolate the term containing y

Begin by subtracting the term that does not contain y from both sides of the equation. The equation is initially given as: \(3x + 2y = 11\)Subtract \(3x\) from both sides to isolate the term containing y:\(2y = 11 - 3x\)

- Solve for y

Next, you need to solve for y by dividing both sides of the equation by 2:\(y = \frac{11 - 3x}{2}\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

isolating variables

In algebra, isolating variables is an essential skill. It allows you to transform an equation to make one variable the subject.

This process involves moving terms from one side of the equation to the other. The goal here is to have the variable you're solving for by itself on one side of the equation.

For example, in the given equation: \(3x + 2y = 11\), the goal is to solve for \(y\).

To isolate \(y\), we subtract the term containing \(x\) (i.e., \(3x\)) from both sides of the equation. This changes the equation to:

\(2y = 11 - 3x\).

Now, \(y\) is isolated with only a coefficient of 2 in front.

solving for y

Once the term containing \(y\) is isolated, the next step is to completely solve for \(y\).

In our equation, we now have \(2y = 11 - 3x\).

To solve for \(y\), you need the variable to be by itself. Currently, \(y\) is still multiplied by 2. To remove the multiplication, divide every term on both sides of the equation by 2.

This results in:
\(y = \frac{11 - 3x}{2}\)

Now, \(y\) is expressed in terms of \(x\). This completes the process of solving for \(y\).

Remember, in solving, always perform the same operation to both sides of the equation to maintain equality.

algebraic manipulation

Algebraic manipulation involves performing operations like addition, subtraction, multiplication, and division to rearrange equations.

The goal is to simplify the equation or solve for a particular variable. Let鈥檚 look at the original equation: \(3x + 2y = 11\).

By subtracting \(3x\) from both sides, we perform subtraction to isolate the term with \(y\):
\(2y = 11 - 3x\)

Next, we divide both sides by 2 to simplify the equation:
\(y = \frac{11 - 3x}{2}\)

This demonstrates both subtraction and division. By consistently applying appropriate operations, algebraic manipulation helps in effectively solving equations. Make sure to perform each step carefully to avoid mistakes.

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91影视

Solve for the formula for \(y\). Solve the formula \(3 x+2 y=11\) for \(y\).

Short Answer

Step by step solution

- Isolate the term containing y

- Solve for y

Key Concepts

isolating variables

solving for y

algebraic manipulation

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