To solve the equation [tex]\(3v + 16 = 60\)[/tex] for [tex]\(v\)[/tex], let's go through the correct steps one by one.
Step 1: Isolate the term with the variable on one side of the equation.
To do this, we need to eliminate the constant term ([tex]\(+16\)[/tex]) on the left-hand side. This can be done by subtracting 16 from both sides of the equation.
[tex]\[
3v + 16 - 16 = 60 - 16
\][/tex]
Simplifying both sides, we get:
[tex]\[
3v = 44
\][/tex]
Step 2: Solve for [tex]\(v\)[/tex] by isolating it completely.
Now, we need to divide both sides by the coefficient of [tex]\(v\)[/tex], which is 3.
[tex]\[
\frac{3v}{3} = \frac{44}{3}
\][/tex]
This simplifies to:
[tex]\[
v = \frac{44}{3}
\][/tex]
Step 3: Verify the solution
It's always a good idea to verify the solution by plugging it back into the original equation to make sure it holds true.
[tex]\[
3 \left(\frac{44}{3}\right) + 16 = 60
\][/tex]
Simplifying the left-hand side:
[tex]\[
44 + 16 = 60
\][/tex]
Since both sides of the equation are equal, our solution [tex]\(v = \frac{44}{3}\)[/tex] is correct.
Thus, the student should have subtracted 16 from both sides in the first step.
The correct operation the student should have performed is:
- Subtracted 16 from both sides.
