Let's solve each equation step by step using the given values for $ x $, $ y $, and $ z $. We'll follow the
order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
---
1. $ (x - 12) \div y + z $
Given: $ x = -23 $, $ y = -5 $, $ z = -10 $
Step 1: Substitute the values:
$$
(-23 - 12) \div (-5) + (-10)
$$
Step 2: Simplify inside parentheses:
$$
(-35) \div (-5) + (-10)
$$
Step 3: Divide:
$$
7 + (-10)
$$
Step 4: Add:
$$
7 - 10 = -3
$$
✔ Answer: $-3$
---
2. $ (2x + 2) \div y * z $
Given: $ x = 6 $, $ y = 7 $, $ z = 12 $
Step 1: Substitute:
$$
(2(6) + 2) \div 7 * 12
$$
Step 2: Simplify inside parentheses:
$$
(12 + 2) \div 7 * 12 = 14 \div 7 * 12
$$
Step 3: Divide and multiply from left to right:
$$
2 * 12 = 24
$$
✔ Answer: $24$
> Note: Multiplication and division are done left to right. So $ 14 \div 7 = 2 $, then $ 2 * 12 = 24 $.
---
3. $ (4x - 17) \div y - z $
Given: $ x = 8 $, $ y = 5 $, $ z = 3 $
Step 1: Substitute:
$$
(4(8) - 17) \div 5 - 3
$$
Step 2: Simplify inside parentheses:
$$
(32 - 17) \div 5 - 3 = 15 \div 5 - 3
$$
Step 3: Divide:
$$
3 - 3 = 0
$$
✔ Answer: $0$
---
4. $ (2x - 6) \div y * z $
Given: $ x = 12 $, $ y = 6 $, $ z = 4 $
Step 1: Substitute:
$$
(2(12) - 6) \div 6 * 4
$$
Step 2: Simplify inside parentheses:
$$
(24 - 6) \div 6 * 4 = 18 \div 6 * 4
$$
Step 3: Divide and multiply left to right:
$$
3 * 4 = 12
$$
✔ Answer: $12$
---
✔ Final Answers:
1. $-3$
2. $24$
3. $0$
4. $12$
Let me know if you'd like this formatted as a completed worksheet!
Parent Tip: Review the logic above to help your child master the concept of algebra 1 printouts.
