QuestionSolve the equation. $-4(-2 v+3)=28$

Studdy Solution

STEP 1

What is this asking? We need to find the value of $v$ that makes the equation $-4(-2v + 3) = 28$ true. Watch out! Be careful with the signs when distributing!
A negative times a negative is a positive, and a negative times a positive is a negative.

STEP 2

1. Distribute
2. Isolate the term with $v$
3. Solve for $v$

STEP 3

Alright, let's kick things off by distributing that $-4$ into the parentheses!
Remember, distributing means multiplying the $-4$ by each term inside the parentheses.

STEP 4

$-4 \cdot (-2v) + (-4) \cdot 3 = 28$ So, $-4$ times $-2v$ gives us $8v$ , and $-4$ times $3$ gives us $-12$ .

STEP 5

Our equation now looks like this: $8v - 12 = 28$ Much cleaner, right?

STEP 6

Next, we want to get that $v$ term all by itself.
Let's add $12$ to both sides of the equation to move that $-12$ over to the right.
Remember, what we do to one side, we must do to the other to keep things balanced!

STEP 7

$8v - 12 + 12 = 28 + 12$ Notice how $-12 + 12$ becomes zero.
This is what we wanted.

STEP 8

Now we have: $8v = 40$ We're almost there!

STEP 9

Finally, to get $\boldsymbol{v}$ all alone, we need to divide both sides of the equation by $8$ .

STEP 10

$\frac{8v}{8} = \frac{40}{8}$ Since $\frac{8}{8}$ is $1$ , we have $1$ times $v$ on the left side, which is just $v$ .
Perfect!

STEP 11

And on the right side, $\frac{40}{8}$ gives us $5$ .

STEP 12

$v = 5$ Boom! We found it!

STEP 13

The solution to the equation $-4(-2v + 3) = 28$ is $v = 5$ .

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