Problem: Evaluate the given equations using the provided values for \( x \), \( y \), and \( z \).
####
Equation 1:
\[
(x - 12) \div y + z
\]
Given: \( x = 23 \), \( y = 5 \), \( z = -10 \)
Step-by-Step Solution:
1. Substitute the given values into the equation:
\[
(23 - 12) \div 5 + (-10)
\]
2. Simplify inside the parentheses:
\[
23 - 12 = 11
\]
So the equation becomes:
\[
11 \div 5 + (-10)
\]
3. Perform the division:
\[
11 \div 5 = 2.2
\]
So the equation now is:
\[
2.2 + (-10)
\]
4. Perform the addition:
\[
2.2 - 10 = -7.8
\]
Final Answer for Equation 1:
\[
\boxed{-7.8}
\]
---
####
Equation 2:
\[
(2x + 2) \div y \times z
\]
Given: \( x = 6 \), \( y = 7 \), \( z = 12 \)
Step-by-Step Solution:
1. Substitute the given values into the equation:
\[
(2 \cdot 6 + 2) \div 7 \times 12
\]
2. Simplify inside the parentheses:
\[
2 \cdot 6 = 12
\]
So:
\[
12 + 2 = 14
\]
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 Equation 2:
\[
\boxed{24}
\]
---
####
Equation 3:
\[
(4x - 17) \div y - z
\]
Given: \( x = 8 \), \( y = 5 \), \( z = 3 \)
Step-by-Step Solution:
1. Substitute the given values into the equation:
\[
(4 \cdot 8 - 17) \div 5 - 3
\]
2. Simplify inside the parentheses:
\[
4 \cdot 8 = 32
\]
So:
\[
32 - 17 = 15
\]
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 Equation 3:
\[
\boxed{0}
\]
---
####
Equation 4:
\[
(2x - 6) \div y \times z
\]
Given: \( x = 12 \), \( y = 6 \), \( z = 4 \)
Step-by-Step Solution:
1. Substitute the given values into the equation:
\[
(2 \cdot 12 - 6) \div 6 \times 4
\]
2. Simplify inside the parentheses:
\[
2 \cdot 12 = 24
\]
So:
\[
24 - 6 = 18
\]
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 Equation 4:
\[
\boxed{12}
\]
---
Final Answers:
1. \(\boxed{-7.8}\)
2. \(\boxed{24}\)
3. \(\boxed{0}\)
4. \(\boxed{12}\)
Parent Tip: Review the logic above to help your child master the concept of fun algebra worksheet.
