Problem: Solve the linear equations from the worksheet.
####
Worksheet Problems:
1. \( k + 9 = 7 \)
2. \( 6 + t = 1 \)
3. \( 1 \cdot 6 = b - 8 \)
4. \( y + 11 = 9 \)
5. \( 12 = \frac{x}{5} \)
6. \( 11n - 6n = 6 \)
7. \( 7 = a + 6 \)
8. \( \frac{s}{10} = 7 \)
---
Solution:
####
1. \( k + 9 = 7 \)
To solve for \( k \):
- Subtract 9 from both sides:
\[
k + 9 - 9 = 7 - 9
\]
\[
k = -2
\]
Answer: \( k = -2 \)
---
####
2. \( 6 + t = 1 \)
To solve for \( t \):
- Subtract 6 from both sides:
\[
6 + t - 6 = 1 - 6
\]
\[
t = -5
\]
Answer: \( t = -5 \)
---
####
3. \( 1 \cdot 6 = b - 8 \)
Simplify the left side:
\[
6 = b - 8
\]
To solve for \( b \):
- Add 8 to both sides:
\[
6 + 8 = b - 8 + 8
\]
\[
b = 14
\]
Answer: \( b = 14 \)
---
####
4. \( y + 11 = 9 \)
To solve for \( y \):
- Subtract 11 from both sides:
\[
y + 11 - 11 = 9 - 11
\]
\[
y = -2
\]
Answer: \( y = -2 \)
---
####
5. \( 12 = \frac{x}{5} \)
To solve for \( x \):
- Multiply both sides by 5:
\[
12 \cdot 5 = \frac{x}{5} \cdot 5
\]
\[
x = 60
\]
Answer: \( x = 60 \)
---
####
6. \( 11n - 6n = 6 \)
Simplify the left side:
\[
(11 - 6)n = 6
\]
\[
5n = 6
\]
To solve for \( n \):
- Divide both sides by 5:
\[
\frac{5n}{5} = \frac{6}{5}
\]
\[
n = \frac{6}{5}
\]
Answer: \( n = \frac{6}{5} \)
---
####
7. \( 7 = a + 6 \)
To solve for \( a \):
- Subtract 6 from both sides:
\[
7 - 6 = a + 6 - 6
\]
\[
a = 1
\]
Answer: \( a = 1 \)
---
####
8. \( \frac{s}{10} = 7 \)
To solve for \( s \):
- Multiply both sides by 10:
\[
\frac{s}{10} \cdot 10 = 7 \cdot 10
\]
\[
s = 70
\]
Answer: \( s = 70 \)
---
Final Answers:
\[
\boxed{
\begin{aligned}
1. & \ k = -2 \\
2. & \ t = -5 \\
3. & \ b = 14 \\
4. & \ y = -2 \\
5. & \ x = 60 \\
6. & \ n = \frac{6}{5} \\
7. & \ a = 1 \\
8. & \ s = 70
\end{aligned}
}
\]
Parent Tip: Review the logic above to help your child master the concept of online algebra worksheet.
