Explanation:
In the given expression 1/6 is negative, because it's inside a parenthesis which has a negative sign before. In the same way, 4 is positive because it's negative inside the parenthesis but with the negative sign it becomes positive. And finally 1/3 is negative.
[tex]-\frac{1}{3}+4-\frac{1}{6}[/tex]Now we have to look at the options:
• A. ,It's not equivalent because there are no parenthesis and the signs don't match ( for example, 4 is negative and it has to be positive)
,• B., It's not equivalent because 1/6 is positive and it has to be negative. Even if the other two numbers have the right sign.
,• C., We have to eliminate the parenthesis first:
[tex]-(\frac{1}{3}-\frac{1}{6})+4=-\frac{1}{3}+\frac{1}{6}+4[/tex]The sign of 1/6 is not right either.
• D., This is the same expression I wrote at the beginning of the explanation just in a different order, so this is equivalent
,• E., We have to do the same as option C:
[tex]-\frac{1}{3}-(4-\frac{1}{6})=-\frac{1}{3}-4+\frac{1}{6}[/tex]The signs of 4 and 1/6 are wrong, so this is not equivalent.
• F., We do the same as before:
[tex]4-(\frac{1}{3}+\frac{1}{6})=4-\frac{1}{3}-\frac{1}{6}[/tex]This expression is equivalent
Answer:
The equivalent expressions are options D and F
