Suppose [tex]a[/tex] and [tex]b[/tex] are real numbers where [tex]a > 0[/tex] and [tex]b < 0[/tex].

a. Is [tex]-a + b[/tex] positive or negative? Explain how you know.

b. Is [tex]a - b[/tex] positive or negative? Explain how you know.

c. Is [tex]b - a[/tex] positive or negative? Explain how you know.

a is positive and b is negative from the info that they tell us a. negative a has to be negative because of the sign and b is going to be negative, so there is no way that there is going to be a positive if both are negative b. positive a is going to be positive because it says it in the beginning sentence it is and two negatives from the equation and b make a positive, so it is two positives c. negative b is negative and a is negative from the sign in the equation which make two negatives

Answered by theapplezoo | 2024-06-10

The evaluations show that − a + b is negative, a − b is positive, and b − a is negative. Therefore, the signs of the expressions depend on the values of a and b given their respective conditions. Each conclusion follows logically from the definitions of positive and negative numbers.
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Answered by theapplezoo | 2024-10-01