Leee01idn
Answered

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A student is asked to solve the equation [tex]3c - 16 = 53[/tex] for [tex]c[/tex]. Their work is shown.

\begin{tabular}{|l|r|}
\hline
Original Problem & [tex]3c - 16 = 53[/tex] \\
\hline
Step One & [tex]+16 + 16[/tex] \\
\hline
Step Two & [tex]3c = 69[/tex] \\
\hline
Step Three & [tex](3) 3c = 69(3)[/tex] \\
\hline
Step Four & [tex]c = 207[/tex] \\
\hline
\end{tabular}

The student made a mistake in Step Three. What operation should the student have performed?

A. Added 3 to both sides
B. Multiplied by 69 on both sides
C. Divided by 3 on both sides
D. Subtracted 69 on both sides

Sagot :

GinnyAnsweridn
Let's solve the problem step by step, identifying the correct operations along the way.

We start with the equation:
[tex]\[ 3c - 16 = 53 \][/tex]

Step One: Add 16 to both sides of the equation to isolate the term with [tex]\( c \)[/tex].
[tex]\[ 3c - 16 + 16 = 53 + 16 \][/tex]
This simplifies to:
[tex]\[ 3c = 69 \][/tex]

Step Two: At this point, we have:
[tex]\[ 3c = 69 \][/tex]

Step Three: The correct operation to isolate [tex]\( c \)[/tex] is to divide both sides of the equation by 3, not multiply:
[tex]\[ \frac{3c}{3} = \frac{69}{3} \][/tex]
This simplifies to:
[tex]\[ c = 23 \][/tex]

So, the correct operation that the student should have performed in Step Three is to divide both sides by 3.
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