IDNLearn.com makes it easy to get reliable answers from experts and enthusiasts alike. Ask your questions and receive prompt, detailed answers from our experienced and knowledgeable community members.

Marcus tried to solve an equation.

[tex]\[
\begin{aligned}
2.5b & = 5 \\
\frac{2.5b}{2.5} & = \frac{5}{2.5} \\
b & = 3
\end{aligned}
\][/tex]

Where did Marcus make his first mistake?

Choose one answer:
(A) Setting up
(B) Calculating
(C) Marcus correctly solved the equation.


Sagot :

Sure, let's analyze the steps Marcus took to solve the equation and understand where he might have made an error.

1. Original Equation:
[tex]\[ 2.5b = 5 \][/tex]

This equation is correctly set up. Nothing wrong here.

2. Dividing both sides by 2.5 to isolate [tex]\( b \)[/tex]:
[tex]\[ \frac{2.5b}{2.5} = \frac{5}{2.5} \][/tex]

Simplifying the left-hand side, we get:
[tex]\[ b = \frac{5}{2.5} \][/tex]

3. Calculating [tex]\( \frac{5}{2.5} \)[/tex]:

This is the crucial step. Marcus needs to compute:
[tex]\[ \frac{5}{2.5} \][/tex]

To do this division correctly:
[tex]\[ \frac{5}{2.5} = 2 \][/tex]
So, [tex]\( b = 2 \)[/tex].

4. Marcus’ Result:
Marcus wrote [tex]\( b = 3 \)[/tex]. This is incorrect because:
[tex]\[ b = 2 \][/tex]

Therefore, Marcus made his mistake during the calculation step. The correct calculation of [tex]\( \frac{5}{2.5} \)[/tex] should yield 2, not 3.

So, the correct answer is:
(B) Calculating