Final answer:
To create an equivalent expression for 3z + 2 + (-5z) + 6, combine like terms to get -2z + 8 which involves adding coefficients of z and summing constant terms.
Step-by-step explanation:
To combine like terms and create an equivalent expression for 3z + 2 + (-5z) + 6, we need to add the coefficients of the like terms and keep the constant terms together. The like terms here are 3z and (-5z), which are terms that contain the variable z. To combine them:
- Add the coefficients of z: 3 + (-5) = -2.
- The constant terms are 2 and 6. When added together: 2 + 6 = 8.
The equivalent expression after combining like terms is -2z + 8.
Remember that when combining terms, the addition rules apply based on the signs of the numbers. Adding two negative numbers keeps the negative sign, adding numbers with opposite signs involves subtraction and taking the sign of the larger number, and when subtracting, we change the sign of the subtracted number then add.