Problem 89 - Introductory Algebra for College Students

Question

Find the value of each expression. $$|-9-(-3+7)|-|-17-(-2)|$$

Step-by-Step Solution

Answer

-10

Step 1: Solve the equations inside inner parentheses

For |-9-(-3+7)|-|-17-(-2)|, the content inside the inner parentheses in each absolute value expression are -3+7=-4 in the first absolute value and -2 in the second one. So, rewrite the equation as |-9--4|-|-17--2|.

Step 2: Simplify further by performing subtraction operations

Performing the subtractions gives, |-9--4| becomes |-9+4|=|-5| and |-17--2| becomes |-17+2| = |-15|. So, rewrite equation as |-5| - |-15|.

Step 3: Apply the absolute value definition

As the definition of the absolute value of a number, you end up with 5-15 since absolute value of -5 is 5 and -15 is 15.

Step 4: Perform the subtraction

Perform the subtraction 5-15 = -10. So this is the solution.