Question3a. $7 v-3=5+3(v+2)$

Studdy Solution

STEP 1

What is this asking? Solve for $v$ in the equation $7v - 3 = 5 + 3(v + 2)$ . Watch out! Don't forget to distribute the $3$ to both terms inside the parentheses!

STEP 2

1. Distribute the $3$
2. Simplify both sides
3. Isolate $v$
4. Solve for $v$

STEP 3

Let's distribute the $3$ on the right-hand side of the equation.
We have $3(v + 2)$ , which means we need to multiply $3$ by both $v$ and $2$ .
$3(v + 2) = 3 \cdot v + 3 \cdot 2 = 3v + 6$

STEP 4

Now, rewrite the equation with the distributed terms:
$7v - 3 = 5 + 3v + 6$

STEP 5

Combine like terms on the right-hand side.
Add $5$ and $6$ together:
$7v - 3 = 3v + 11$

STEP 6

Let's move all the $v$ terms to one side and the constants to the other.
Start by subtracting $3v$ from both sides to get all the $v$ terms on the left:
$7v - 3v - 3 = 11$

STEP 7

Simplify the left-hand side:
$4v - 3 = 11$

STEP 8

Now, add $3$ to both sides to get rid of the constant on the left:
$4v = 11 + 3$

STEP 9

Simplify the right-hand side:
$4v = 14$

STEP 10

Finally, divide both sides by $4$ to solve for $v$ :
$v = \frac{14}{4} = \frac{7}{2}$

STEP 11

The value of $v$ is $\frac{7}{2}$ .

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