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Math  /  Algebra

QuestionSolve for yy. 4=−3y+24=-\frac{3}{y+2}
Simplify your answer as much as possible. y=y= No solution □\sqrt{\square} □\square □\square □\square

Studdy Solution

STEP 1

What is this asking? We need to find the value of yy that makes the equation 4=−3y+24 = -\frac{3}{y+2} true. Watch out! Be careful when multiplying and dividing by negative numbers, and remember that dividing by zero is a no-no!

STEP 2

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

STEP 3

We want to get (y+2)(y+2) out of the denominator.
To do that, we can **multiply both sides** of the equation by (y+2)(y+2).
Remember, whatever we do to one side, we *must* do to the other to keep the equation balanced! 4⋅(y+2)=−3y+2⋅(y+2)4 \cdot (y+2) = -\frac{3}{y+2} \cdot (y+2) 4⋅(y+2)=−34 \cdot (y+2) = -3

STEP 4

Now, we want to isolate the (y+2)(y+2) term.
Since it's being multiplied by **4**, we'll **divide both sides** by **4**. 4⋅(y+2)4=−34\frac{4 \cdot (y+2)}{4} = \frac{-3}{4} y+2=−34y+2 = -\frac{3}{4}

STEP 5

Almost there!
We just need to get yy by itself.
Since **2** is being added to yy, we'll **subtract 2** from both sides of the equation. y+2−2=−34−2y + 2 - 2 = -\frac{3}{4} - 2 y=−34−2y = -\frac{3}{4} - 2

STEP 6

To subtract **2** from −34-\frac{3}{4}, we need a common denominator.
We can rewrite **2** as 84\frac{8}{4} since 2⋅4=82 \cdot 4 = 8.
Now we have: y=−34−84y = -\frac{3}{4} - \frac{8}{4} y=−3+84y = -\frac{3+8}{4}y=−114y = -\frac{11}{4}And there we have it!

STEP 7

y=−114y = -\frac{11}{4}

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