Studdy AI Logo
Math  /  Algebra

QuestionSolve for yy. 4+7y=534+\frac{7}{y}=\frac{5}{3}
Simplify your answer as much as possible. y=y=

Studdy Solution

STEP 1

What is this asking? We need to find the value of yy that makes the equation 4+7y=534 + \frac{7}{y} = \frac{5}{3} true. Watch out! Remember, we can't divide by **zero**, so yy cannot be zero!

STEP 2

1. Isolate the term with yy.
2. Multiply both sides to get yy out of the denominator.
3. Isolate yy.

STEP 3

Alright, let's **isolate** that 7y\frac{7}{y} term!
We've got 44 added to it, so we'll subtract 44 from both sides of the equation.
Why both sides?
Gotta keep things **balanced**! 4+7y−4=53−44 + \frac{7}{y} - 4 = \frac{5}{3} - 4 7y=53−4 \frac{7}{y} = \frac{5}{3} - 4

STEP 4

Now, let's simplify that right side.
Remember, 44 is the same as 41\frac{4}{1}.
To subtract fractions, we need a **common denominator**.
In this case, it's **3**. 7y=53−4⋅31⋅3 \frac{7}{y} = \frac{5}{3} - \frac{4 \cdot 3}{1 \cdot 3} 7y=53−123 \frac{7}{y} = \frac{5}{3} - \frac{12}{3}7y=5−123 \frac{7}{y} = \frac{5 - 12}{3}7y=−73 \frac{7}{y} = \frac{-7}{3}

STEP 5

That yy is hiding in the denominator!
Let's bring it up top by multiplying both sides by yy.
Remember, what we do to one side, we do to the other! 7y⋅y=−73⋅y \frac{7}{y} \cdot y = \frac{-7}{3} \cdot y 7=−73⋅y 7 = \frac{-7}{3} \cdot y

STEP 6

Now, let's get rid of that **3** in the denominator on the right side by multiplying both sides by **3**. 7⋅3=−73⋅y⋅37 \cdot 3 = \frac{-7}{3} \cdot y \cdot 3 21=−7⋅y21 = -7 \cdot y

STEP 7

Almost there!
We want yy all by itself, so let's **divide** both sides by −7-7. 21−7=−7⋅y−7\frac{21}{-7} = \frac{-7 \cdot y}{-7} 21−7=−7−7⋅y\frac{21}{-7} = \frac{-7}{-7} \cdot y−3=1⋅y-3 = 1 \cdot y−3=y-3 = ySo, y=−3y = -3!

STEP 8

y=−3y = -3

Was this helpful?

Studdy solves anything!

banner

Start learning now

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

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord