Question $-\frac{1}{3}(6 y+6)+20=3 y$

Studdy Solution

STEP 1

What is this asking? We need to find the mystery number $y$ that makes this equation true! Watch out! Distributing negatives can be tricky, so be super careful with the signs.

STEP 2

1. Distribute and Simplify
2. Isolate the Variable
3. Solve for $y$

STEP 3

Alright, let's kick things off by distributing that $-\frac{1}{3}$ to both terms inside the parentheses.
Remember, multiplying by $-\frac{1}{3}$ is the same as dividing by $-3$ .
So, we've got: $-\frac{1}{3} \cdot 6y + \left( -\frac{1}{3} \right) \cdot 6 + 20 = 3y$ $-2y - 2 + 20 = 3y$

STEP 4

Now, let's tidy things up a bit by combining those constant terms on the left side.
We have $-2$ and $+20$ , which add up to $+18$ : $-2y + 18 = 3y$

STEP 5

Let's get all the $y$ terms together on one side of the equation.
We can do this by adding $2y$ to both sides.
This way, we keep everything balanced: $-2y + 18 + 2y = 3y + 2y$ $18 = 5y$

STEP 6

Almost there!
Now, we just need to isolate $y$ .
We can do this by dividing both sides of the equation by $5$ : $\frac{18}{5} = \frac{5y}{5}$ $\frac{18}{5} = y$

STEP 7

So, our mystery number is $y = \frac{18}{5}$ !
We did it!

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