To solve the given problems, we will evaluate each equation step by step using the provided values for \( x \), \( y \), and \( z \). Let's go through each problem:
---
Problem 1:
Evaluate \((x - 12) \div y + z\) for \( x = -23 \), \( y = -5 \), and \( z = -10 \).
#### Step-by-Step Solution:
1. Substitute the given values into the equation:
\[
(x - 12) \div y + z = ((-23) - 12) \div (-5) + (-10)
\]
2. Simplify inside the parentheses:
\[
(-23) - 12 = -35
\]
So the equation becomes:
\[
(-35) \div (-5) + (-10)
\]
3. Perform the division:
\[
(-35) \div (-5) = 7
\]
So the equation now is:
\[
7 + (-10)
\]
4. Perform the addition:
\[
7 + (-10) = -3
\]
#### Final Answer for Problem 1:
\[
\boxed{-3}
\]
---
Problem 2:
Evaluate \((2x + 2) \div y \times z\) for \( x = 6 \), \( y = 7 \), and \( z = 12 \).
#### Step-by-Step Solution:
1. Substitute the given values into the equation:
\[
(2x + 2) \div y \times z = (2(6) + 2) \div 7 \times 12
\]
2. Simplify inside the parentheses:
\[
2(6) + 2 = 12 + 2 = 14
\]
So the equation becomes:
\[
14 \div 7 \times 12
\]
3. Perform the division:
\[
14 \div 7 = 2
\]
So the equation now is:
\[
2 \times 12
\]
4. Perform the multiplication:
\[
2 \times 12 = 24
\]
#### Final Answer for Problem 2:
\[
\boxed{24}
\]
---
Problem 3:
Evaluate \((4x - 17) \div y - z\) for \( x = 8 \), \( y = 5 \), and \( z = 3 \).
#### Step-by-Step Solution:
1. Substitute the given values into the equation:
\[
(4x - 17) \div y - z = (4(8) - 17) \div 5 - 3
\]
2. Simplify inside the parentheses:
\[
4(8) - 17 = 32 - 17 = 15
\]
So the equation becomes:
\[
15 \div 5 - 3
\]
3. Perform the division:
\[
15 \div 5 = 3
\]
So the equation now is:
\[
3 - 3
\]
4. Perform the subtraction:
\[
3 - 3 = 0
\]
#### Final Answer for Problem 3:
\[
\boxed{0}
\]
---
Problem 4:
Evaluate \((2x - 6) \div y \times z\) for \( x = 12 \), \( y = 6 \), and \( z = 4 \).
#### Step-by-Step Solution:
1. Substitute the given values into the equation:
\[
(2x - 6) \div y \times z = (2(12) - 6) \div 6 \times 4
\]
2. Simplify inside the parentheses:
\[
2(12) - 6 = 24 - 6 = 18
\]
So the equation becomes:
\[
18 \div 6 \times 4
\]
3. Perform the division:
\[
18 \div 6 = 3
\]
So the equation now is:
\[
3 \times 4
\]
4. Perform the multiplication:
\[
3 \times 4 = 12
\]
#### Final Answer for Problem 4:
\[
\boxed{12}
\]
---
Final Answers:
1. \(\boxed{-3}\)
2. \(\boxed{24}\)
3. \(\boxed{0}\)
4. \(\boxed{12}\)
Parent Tip: Review the logic above to help your child master the concept of algebra equations worksheet with answers.
