Question

What is (5/6z+5)+(−1/3z−4) ? Explain how you found your answer. Include in your explanation any properties that you used to simplify the expression. Skip to input field

Answer 1

To simplify (5/6z+5)+(−1/3z−4), find a common denominator to combine the 'z' terms, resulting in 1/2z, and then add the constants to get a simplified expression of 1/2z + 1.

Step-by-step explanation:

To combine the algebraic expressions (5/6z+5) + (−1/3z−4), we need to simplify by combining like terms. This involves adhering to the rules of addition for coefficients and constants while ensuring that the variable portions ('z' terms) are combined separately from the constant terms.

1. First, identify like terms, which are terms that have the same variable raised to the same power. In this case, 5/6z and −1/3z are like terms because they both contain the variable 'z' to the first power.
2. Next, find a common denominator for the coefficients of 'z'. The common denominator for 6 and 3 is 6, so −1/3z becomes −2/6z after multiplying the numerator and denominator by 2.
3. Now we can combine the like terms. Adding 5/6z and −2/6z results in (5−2)/6z = 3/6z or 1/2z after simplifying.
4. Finally, add the constant terms, 5 and −4, resulting in 1.

The complete simplified expression is 1/2z + 1.

Throughout the process, we applied the associative property of addition to group like terms, the commutative property of addition when rearranging terms, and we simplified fractions according to standard arithmetic rules.