Kate simplified the absolute value expression $$|-1-2|-\big||-3|-4\big|$$ in the following steps:
(1) She removed the nested absolute value as follows: $$|-1-2|-|3-4|$$
(2) Then she removed the remaining absolute values. The absolute value turns negative numbers into positive numbers. $$1+2-(3+4)$$
(3) She removed the parentheses as follows: $$1+2-3-4$$
(4) Finally, she found the sum of the numbers: $$1+2-3-4=-4$$
Is her solution correct? If not, identify all her mistakes.
Yes. The whole solution is perfectly fine.
No, her solution is not correct. The mistake is in step (2). The correct solution is: $$|-1-2|-|3-4|=|-3|-|-1|=3+1=4$$
No, her solution is not correct. The mistake is in step (2). The correct solution is: $$|-1-2|-|3-4|=|-3|-|-1|=3-1=2$$
No, her solution is not correct. The mistake is in step (3). The correct solution is: $$1+2-(3+4)=1+2-3+4=4$$
Correct solution:
$$|-1-2|-\big||-3|-4\big|=|-3|-|3-4|=|-3|-|-1|=3-1=2$$