Chapter 4.9, Problem 4MRE

To determine

To simplify: the given algebraic expression

Answer to Problem 4MRE

The simplified algebraic expression is $\boxed{14}$

Explanation of Solution

Given information: $y-\left(-7\right)-\left[y+\left(-7\right)\right]$

Concept Involved:

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.

When adding like terms we need to add their coefficients.

Calculation: Distribute the negative in the expression $y-\left(-7\right)-\left[y+\left(-7\right)\right]$

  $y+7-y-\left(-7\right)$

Group like terms

  $y-y+7-\left(-7\right)$

Turn the subtraction problem to an addition problem by changing the sign of the term we are subtracting

  $y+\left(-y\right)+7+\left(+7\right)$

Combine like terms

  $14$

Conclusion:

The algebraic expression $y-\left(-7\right)-\left[y+\left(-7\right)\right]$ is simplified to give $\boxed{14}$