Question6) $7 v+8(7 v-8)=-379$

Studdy Solution

STEP 1

What is this asking? We need to find the mystery number $v$ that makes the equation $7v + 8(7v - 8) = -379$ true! Watch out! Don't forget to distribute correctly, and watch those negative signs!

STEP 2

1. Simplify the equation
2. Isolate the variable term
3. Solve for v

STEP 3

Let's distribute that $8$ across the terms inside the parentheses.
Remember, distributing means multiplying the $8$ by both the $7v$ and the $-8$ .
This gives us $8 \cdot 7v = 56v$ and $8 \cdot (-8) = -64$ .
So, our equation becomes $7v + 56v - 64 = -379$ .

STEP 4

Now, let's combine those v terms!
We have $7v$ and $56v$ , and adding them together gives us $7v + 56v = 63v$ .
Our equation is now much simpler: $63v - 64 = -379$ .

STEP 5

We want that $v$ all alone!
To get rid of the $-64$ on the left side, we'll add $64$ to both sides of the equation.
Remember, what we do to one side, we must do to the other to keep things balanced!
This gives us $63v - 64 + 64 = -379 + 64$ .
Simplifying, we get $63v = -315$ .

STEP 6

We're almost there!
Now, we just need to divide both sides of the equation by $63$ to isolate $v$ .
This is because $\frac{63}{63}=1$ , and we want $1v$ .
So, we have $\frac{63v}{63} = \frac{-315}{63}$ .

STEP 7

Dividing $-315$ by $63$ gives us $v = -5$ .
Boom! We found it!

STEP 8

$v = -5$

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