QuestionSolve $10(2 y+2)-y=2(8 y-8)$ .
The solution is $y=$

Studdy Solution

STEP 1

What is this asking? We're asked to solve for the unknown variable $y$ in a single equation. Watch out! Don't forget to distribute correctly across the parentheses and keep track of your signs!

STEP 2

1. Expand both sides
2. Group like terms
3. Isolate $y$
4. Find $y$

STEP 3

Let's expand the left side of the equation: $10(2y + 2) - y$ .
Distributing the 10 across the parentheses gives us $10 \cdot 2y + 10 \cdot 2 - y$ , which simplifies to $20y + 20 - y$ .

STEP 4

Now, let's expand the right side: $2(8y - 8)$ .
Distributing the 2 gives us $2 \cdot 8y - 2 \cdot 8$ , which simplifies to $16y - 16$ .

STEP 5

So, our equation becomes $20y + 20 - y = 16y - 16$ .
Much better!

STEP 6

On the left side, we combine the $y$ terms: $20y - y$ , which gives us $19y$ .
So, our equation is now $19y + 20 = 16y - 16$ .

STEP 7

Let's move all the $y$ terms to the left side.
We can do this by adding $-16y$ to both sides: $19y + 20 + (-16y) = 16y - 16 + (-16y)$ .
This simplifies to $3y + 20 = -16$ .

STEP 8

Now, let's move the constant terms to the right side.
We add $-20$ to both sides: $3y + 20 + (-20) = -16 + (-20)$ .
This simplifies to $3y = -36$ .

STEP 9

To isolate $y$ , we divide both sides of the equation $3y = -36$ by 3: $\frac{3y}{3} = \frac{-36}{3}$ .

STEP 10

This gives us our final answer: $y = -12$ .
Awesome!

STEP 11

$y = -12$

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