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].
