Math / Algebra

Question $3 x-2=4 y+5$

Studdy Solution

STEP 1

What is this asking? We're asked to solve for $x$ in terms of $y$ , meaning we want to get $x$ all alone on one side of the equation. Watch out! Don't mix up $x$ and $y$ when rearranging the equation!

STEP 2

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

STEP 3

Alright, so we've got $3x - 2 = 4y + 5$ .
Our goal is to get $x$ by itself.
First, let's tackle that $-2$ on the left side.
We want to move it over to the right side, and to do that, we'll add $2$ to both sides of the equation.
Remember, what we do to one side, we must do to the other to keep things balanced!

STEP 4

So, adding $2$ to both sides gives us: $3x - 2 + 2 = 4y + 5 + 2$ $3x = 4y + 7$ Great! Now we have $3x$ all by itself on the left.

STEP 5

Now, we have $3x = 4y + 7$ .
We're so close to getting $x$ alone.
We're multiplying $x$ by $3$ , so to undo that, we'll divide both sides by $3$ .
This is the key step to isolating our variable, $x$ !

STEP 6

Dividing both sides by $3$ gives us: $\frac{3x}{3} = \frac{4y + 7}{3}$ $x = \frac{4y + 7}{3}$ Boom! We did it!
We've successfully solved for $x$ in terms of $y$ .

STEP 7

Our final answer is $x = \frac{4y + 7}{3}$ .

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Question $3 x-2=4 y+5$

Studdy Solution

STEP 1

What is this asking? We're asked to solve for $x$ in terms of $y$ , meaning we want to get $x$ all alone on one side of the equation. Watch out! Don't mix up $x$ and $y$ when rearranging the equation!

STEP 2

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

STEP 3

STEP 4

So, adding $2$ to both sides gives us: $3x - 2 + 2 = 4y + 5 + 2$ $3x = 4y + 7$ Great! Now we have $3x$ all by itself on the left.

STEP 5

Now, we have $3x = 4y + 7$ .
We're so close to getting $x$ alone.
We're multiplying $x$ by $3$ , so to undo that, we'll divide both sides by $3$ .
This is the key step to isolating our variable, $x$ !

STEP 6

Dividing both sides by $3$ gives us: $\frac{3x}{3} = \frac{4y + 7}{3}$ $x = \frac{4y + 7}{3}$ Boom! We did it!
We've successfully solved for $x$ in terms of $y$ .

STEP 7

Our final answer is $x = \frac{4y + 7}{3}$ .

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Question3x−2=4y+53 x-2=4 y+53x−2=4y+5

Studdy Solution

STEP 1

What is this asking? We're asked to solve for xxx in terms of yyy, meaning we want to get xxx all alone on one side of the equation. Watch out! Don't mix up xxx and yyy when rearranging the equation!

STEP 2

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

STEP 3

STEP 4

So, adding 222 to both sides gives us: 3x−2+2=4y+5+23x - 2 + 2 = 4y + 5 + 23x−2+2=4y+5+2 3x=4y+73x = 4y + 73x=4y+7Great! Now we have 3x3x3x all by itself on the left.

STEP 5

Now, we have 3x=4y+73x = 4y + 73x=4y+7.We're *so* close to getting xxx alone.We're multiplying xxx by 333, so to undo that, we'll divide *both* sides by 333.This is the key step to isolating our variable, xxx!

STEP 6

Dividing both sides by 333 gives us: 3x3=4y+73\frac{3x}{3} = \frac{4y + 7}{3}33x​=34y+7​ x=4y+73x = \frac{4y + 7}{3}x=34y+7​Boom! We did it!We've successfully solved for xxx in terms of yyy.

STEP 7

Our final answer is x=4y+73x = \frac{4y + 7}{3}x=34y+7​.

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Question $3 x-2=4 y+5$

What is this asking? We're asked to solve for $x$ in terms of $y$ , meaning we want to get $x$ all alone on one side of the equation. Watch out! Don't mix up $x$ and $y$ when rearranging the equation!

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

So, adding $2$ to both sides gives us: $3x - 2 + 2 = 4y + 5 + 2$ $3x = 4y + 7$ Great! Now we have $3x$ all by itself on the left.

Now, we have $3x = 4y + 7$ .
We're so close to getting $x$ alone.
We're multiplying $x$ by $3$ , so to undo that, we'll divide both sides by $3$ .
This is the key step to isolating our variable, $x$ !

Dividing both sides by $3$ gives us: $\frac{3x}{3} = \frac{4y + 7}{3}$ $x = \frac{4y + 7}{3}$ Boom! We did it!
We've successfully solved for $x$ in terms of $y$ .

Our final answer is $x = \frac{4y + 7}{3}$ .