In which step below does a mistake first appear in simplifying the expression?
0.5(-12c+6)-3(c+4)+10(c-5)
Step 1: -6c+3-3(c+4)+10(c-5)
Step 2: -6c+3-3c-12+10(c-5)
Step 3: -6c+3-3c-12+10c-50
Step 4: 7c-41
Please help me!!! Thank you!!
need help
The mistake first appears in Step 2: -6c+3-3c-12+10(c-5).
In this step, the distributive property is incorrectly applied to the term -3(c+4). The correct simplification would be -6c+3-3c-12-10.
So, the correct expression should be -6c+3-3c-12-10(c-5)= -6c+3-3c-12-10c+50= -19c+41.
Therefore, the mistake is in Step 2, where the term '-10' is mistakenly written as '+10'.
To determine in which step a mistake first appears in simplifying the expression, we need to review each step carefully.
Step 1: -6c + 3 - 3(c + 4) + 10(c - 5)
Step 2: -6c + 3 - 3c - 12 + 10(c - 5)
Step 3: -6c + 3 - 3c - 12 + 10c - 50
Step 4: 7c - 41
To find the mistake, we can compare each step with the previous one.
Step 2 introduces the distributive property incorrectly. The -3 should be multiplied to both terms inside the parentheses (c and 4), not just the c.
So, the corrected version of Step 2 should be:
-6c + 3 - 3c - 12 + 10c - 50
Step 2 (corrected): -6c + 3 - 3c - 12 + 10(c - 5)
Now, we can proceed with the simplification:
-6c + 3 - 3c - 12 + 10(c - 5)
= -6c + 3 - 3c - 12 + 10c - 50
= (-6c - 3c + 10c) + (3 - 12 - 50)
= (-9c + 10c) + (-59)
= c - 59
Therefore, in the original steps, the mistake first appears in Step 2.