Math / Algebra

QuestionSolve for $y$ in terms of $x$ . $\begin{array}{l} 3 x-2 y=8 \\ y=\square \end{array}$

Studdy Solution

STEP 1

What is this asking? We're given an equation with $x$ and $y$ , and we need to rewrite it so $y$ is all alone on one side, expressed in terms of $x$ . Watch out! Don't forget to keep track of those negative signs!
They can be sneaky.

STEP 2

1. Isolate the term with $y$ .
2. Solve for $y$ .

STEP 3

We're starting with $3x - 2y = 8$ .
Our goal here is to get $y$ by itself.

STEP 4

To move the $3x$ to the other side, we'll subtract $3x$ from both sides of the equation.
This gives us $3x - 2y - 3x = 8 - 3x$ .
Remember, whatever we do to one side, we must do to the other!

STEP 5

On the left side, $3x - 3x$ adds to zero, leaving us with $-2y$ .
So, our equation now looks like $-2y = 8 - 3x$ .
We're getting closer to having $y$ all alone!

STEP 6

Now, we need to get rid of that $-2$ attached to the $y$ .
We can do this by dividing both sides of the equation by $-2$ .
This gives us $\frac{-2y}{-2} = \frac{8 - 3x}{-2}$ .
Dividing $-2$ by $-2$ gives us $1$ , which is exactly what we want!

STEP 7

On the left side, we have $\frac{-2y}{-2} = 1 \cdot y = y$ , which is exactly what we were aiming for!
On the right side, we have $\frac{8 - 3x}{-2}$ .
We can rewrite this as $\frac{8}{-2} - \frac{3x}{-2}$ .
This simplifies to $-4 + \frac{3}{2}x$ , or $\frac{3}{2}x - 4$ .

STEP 8

So, our final equation is $y = \frac{3}{2}x - 4$ .
We've successfully isolated $y$ and expressed it in terms of $x$ !

STEP 9

$y = \frac{3}{2}x - 4$

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QuestionSolve for $y$ in terms of $x$ . $\begin{array}{l} 3 x-2 y=8 \\ y=\square \end{array}$

Studdy Solution

STEP 1

What is this asking? We're given an equation with $x$ and $y$ , and we need to rewrite it so $y$ is all alone on one side, expressed in terms of $x$ . Watch out! Don't forget to keep track of those negative signs!
They can be sneaky.

STEP 2

1. Isolate the term with $y$ .
2. Solve for $y$ .

STEP 3

We're starting with $3x - 2y = 8$ .
Our goal here is to get $y$ by itself.

STEP 4

To move the $3x$ to the other side, we'll subtract $3x$ from both sides of the equation.
This gives us $3x - 2y - 3x = 8 - 3x$ .
Remember, whatever we do to one side, we must do to the other!

STEP 5

On the left side, $3x - 3x$ adds to zero, leaving us with $-2y$ .
So, our equation now looks like $-2y = 8 - 3x$ .
We're getting closer to having $y$ all alone!

STEP 6

Now, we need to get rid of that $-2$ attached to the $y$ .
We can do this by dividing both sides of the equation by $-2$ .
This gives us $\frac{-2y}{-2} = \frac{8 - 3x}{-2}$ .
Dividing $-2$ by $-2$ gives us $1$ , which is exactly what we want!

STEP 7

On the left side, we have $\frac{-2y}{-2} = 1 \cdot y = y$ , which is exactly what we were aiming for!
On the right side, we have $\frac{8 - 3x}{-2}$ .
We can rewrite this as $\frac{8}{-2} - \frac{3x}{-2}$ .
This simplifies to $-4 + \frac{3}{2}x$ , or $\frac{3}{2}x - 4$ .

STEP 8

So, our final equation is $y = \frac{3}{2}x - 4$ .
We've successfully isolated $y$ and expressed it in terms of $x$ !

STEP 9

$y = \frac{3}{2}x - 4$

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QuestionSolve for yyy in terms of xxx. 3x−2y=8y=□\begin{array}{l} 3 x-2 y=8 \\ y=\square \end{array}3x−2y=8y=□​

Studdy Solution

STEP 1

What is this asking? We're given an equation with xxx and yyy, and we need to rewrite it so yyy is all alone on one side, expressed in terms of xxx. Watch out! Don't forget to keep track of those negative signs!They can be sneaky.

STEP 2

1. Isolate the term with yyy.2. Solve for yyy.

STEP 3

We're starting with 3x−2y=83x - 2y = 83x−2y=8.Our goal here is to get yyy by itself.

STEP 4

To move the 3x3x3x to the other side, we'll subtract 3x3x3x from both sides of the equation.This gives us 3x−2y−3x=8−3x3x - 2y - 3x = 8 - 3x3x−2y−3x=8−3x.Remember, whatever we do to one side, we *must* do to the other!

STEP 5

On the left side, 3x−3x3x - 3x3x−3x adds to zero, leaving us with −2y-2y−2y.So, our equation now looks like −2y=8−3x-2y = 8 - 3x−2y=8−3x.We're getting closer to having yyy all alone!

STEP 6

STEP 7

STEP 8

So, our final equation is y=32x−4y = \frac{3}{2}x - 4y=23​x−4.We've successfully isolated yyy and expressed it in terms of xxx!

STEP 9

y=32x−4y = \frac{3}{2}x - 4y=23​x−4

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve for $y$ in terms of $x$ . $\begin{array}{l} 3 x-2 y=8 \\ y=\square \end{array}$

What is this asking? We're given an equation with $x$ and $y$ , and we need to rewrite it so $y$ is all alone on one side, expressed in terms of $x$ . Watch out! Don't forget to keep track of those negative signs!
They can be sneaky.

1. Isolate the term with $y$ .
2. Solve for $y$ .

We're starting with $3x - 2y = 8$ .
Our goal here is to get $y$ by itself.

To move the $3x$ to the other side, we'll subtract $3x$ from both sides of the equation.
This gives us $3x - 2y - 3x = 8 - 3x$ .
Remember, whatever we do to one side, we must do to the other!

On the left side, $3x - 3x$ adds to zero, leaving us with $-2y$ .
So, our equation now looks like $-2y = 8 - 3x$ .
We're getting closer to having $y$ all alone!

So, our final equation is $y = \frac{3}{2}x - 4$ .
We've successfully isolated $y$ and expressed it in terms of $x$ !

$y = \frac{3}{2}x - 4$