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Answer :
To solve the equation [tex]\(3v + 16 = 60\)[/tex] for [tex]\(v\)[/tex], we need to isolate [tex]\(v\)[/tex] on one side of the equation. Let's go through the correct steps:
1. Step One: The student made a mistake here by dividing by 3 on the left side instead of performing the correct operation. The correct first step is to subtract 16 from both sides of the equation. This operation helps to move the constant term away from the side with the variable.
[tex]\[
3v + 16 - 16 = 60 - 16
\][/tex]
Simplifying both sides:
[tex]\[
3v = 44
\][/tex]
2. Step Two: Now that we have [tex]\(3v = 44\)[/tex], we need to solve for [tex]\(v\)[/tex] by getting rid of the coefficient of [tex]\(v\)[/tex]. We do this by dividing both sides of the equation by 3.
[tex]\[
\frac{3v}{3} = \frac{44}{3}
\][/tex]
Simplifying the left side gives us:
[tex]\[
v = \frac{44}{3}
\][/tex]
If you want to leave it as a fraction, that's fine. But if you need a decimal:
[tex]\[
v \approx 14.67
\][/tex]
Therefore, the correct operation that should have been performed in Step One is to subtract 16 from both sides.
1. Step One: The student made a mistake here by dividing by 3 on the left side instead of performing the correct operation. The correct first step is to subtract 16 from both sides of the equation. This operation helps to move the constant term away from the side with the variable.
[tex]\[
3v + 16 - 16 = 60 - 16
\][/tex]
Simplifying both sides:
[tex]\[
3v = 44
\][/tex]
2. Step Two: Now that we have [tex]\(3v = 44\)[/tex], we need to solve for [tex]\(v\)[/tex] by getting rid of the coefficient of [tex]\(v\)[/tex]. We do this by dividing both sides of the equation by 3.
[tex]\[
\frac{3v}{3} = \frac{44}{3}
\][/tex]
Simplifying the left side gives us:
[tex]\[
v = \frac{44}{3}
\][/tex]
If you want to leave it as a fraction, that's fine. But if you need a decimal:
[tex]\[
v \approx 14.67
\][/tex]
Therefore, the correct operation that should have been performed in Step One is to subtract 16 from both sides.
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