Chapter 4.6, Problem 6MRE

To determine

To evaluate: the value of the expression

Answer to Problem 6MRE

The value of the expression is $\boxed{-2}$

Explanation of Solution

Given information: The expression $w-\left|x-y\right|$ where $w=3;x=-1;$ and $y=4$

Concept Involved:

Substitute the values given for the variable in the expression and simplify

When adding integer with same sign we need find their sum and retain the sign of the larger number to the answer.

When adding integers with different signs we need to find their difference and retain the sign of the larger number to the answer.

When subtracting integers, we need to change the subtraction problem to addition problem by changing the sign of the integer we are subtracting, then following the rules of adding integers.

Calculation: Substituting -1 for x , 4 for y and 3 for w in the expression $w-\left|x-y\right|$

  $3-\left|-1-4\right|$

Rewrite the subtraction problem as an addition problem inside the absolute value expression

  $3-\left|-1+-4\right|$

Adding the integers inside the absolute value expression

  $3-\left|-5\right|$

Drop the absolute value by writing the number inside the absolute value as positive

  $3-5$

Rewrite the subtraction problem as an addition problem

  $3+-5$

Adding the integers

-2

Conclusion:

The value of the given expression $w-\left|x-y\right|$ where $w=3;x=-1;$ and $y=4$is $\boxed{-2}$