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Mira simplified an expression using the strategy shown below.

[tex]\[
\begin{array}{c}
(7-15) \cdot (-5) - 10 \\
(7 \cdot (-5)) - (15 \cdot (-5)) - 10 \\
(-35) - (-75) - 10 \\
40 - 10 \\
30
\end{array}
\][/tex]

What error did Mira make?

A. Mira did not make an error.
B. Mira should have multiplied -5 by -10 first.
C. [tex]\((-35) - (-75) = -110\)[/tex], not 40.
D. [tex]\((7-15) \cdot (-5) \neq (7 \cdot (-5)) - (15 \cdot (-5))\)[/tex]

Sagot :

GinnyAnsweridn
To identify the error Mira made in simplifying the expression, let's carefully follow each step of her work.

1. [tex]\((7 - 15) \cdot (-5) - 10\)[/tex]

2. [tex]\((7 \cdot (-5)) - (15 \cdot (-5)) - 10\)[/tex]

Here, Mira distributed the multiplication over addition: she should have ended up with two separate products inside the subtraction.

3. [tex]\((-35) - (-75) - 10\)[/tex]

Now let's look closely at this step.

- To simplify [tex]\((-35) - (-75)\)[/tex], we must add the opposite:
[tex]\((-35) + 75\)[/tex].

Given that:
[tex]\((-35) - (-75) = -110,\)[/tex] not 40

The error occurred here:

4. 40 - 10

Here Mira added incorrectly, [tex]\((-35) - (-75)\)[/tex] should result in [tex]\(-110\)[/tex]. Hence, 40 is incorrect and thus continuing:

5. 30

Summarizing, the error occurred in the computation of the difference: [tex]\((-35) - (-75) = 40\)[/tex]. The correct calculation should give [tex]\((-35) - (-75) = -110 \)[/tex].

Therefore, the correct identification of Mira's error is:
Mira made the error during the subtraction step [tex]\((-35) - (-75)\)[/tex], which should have resulted in [tex]\(-110, not 40\)[/tex].
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