Question

whole numbers and integers
operations with absolute value: problem type
evaluate the following.
(a) -9 + 7 =
(b) |-9 + 7| =

Explanation:

Part (a)

Step1: Add the two integers

To evaluate \(-9 + 7\), we know that adding a positive number to a negative number is like subtracting the absolute values when the signs are different. The absolute value of \(-9\) is \(9\) and of \(7\) is \(7\). Since \(9>7\), we subtract \(7\) from \(9\) and take the sign of the number with the larger absolute value (which is negative here). So, \(-9 + 7=-(9 - 7)\)

Step2: Calculate the result

\(9 - 7 = 2\), so \(-(9 - 7)=-2\)

Part (b)

Step1: First evaluate the expression inside the absolute value

We already found from part (a) that \(-9 + 7=-2\)

Step2: Take the absolute value

The absolute value of a number is its distance from zero on the number line, so \(\vert -2\vert = 2\)

Answer:

(a) \(-2\)
(b) \(2\)