To solve the given algebraic equations, we need to isolate each variable on one side of the equation. Let's solve each equation step by step.
Equation 1: \( y + 10 = 12 \)
- Subtract 10 from both sides:
\[
y + 10 - 10 = 12 - 10
\]
\[
y = 2
\]
Equation 2: \( c - 3 = 10 \)
- Add 3 to both sides:
\[
c - 3 + 3 = 10 + 3
\]
\[
c = 13
\]
Equation 3: \( -v + 8 = 5 \)
- Subtract 8 from both sides:
\[
-v + 8 - 8 = 5 - 8
\]
\[
-v = -3
\]
- Multiply both sides by -1:
\[
v = 3
\]
Equation 4: \( k - 5 = 12 \)
- Add 5 to both sides:
\[
k - 5 + 5 = 12 + 5
\]
\[
k = 17
\]
Equation 5: \( 3 - t = 1 \)
- Subtract 3 from both sides:
\[
3 - t - 3 = 1 - 3
\]
\[
-t = -2
\]
- Multiply both sides by -1:
\[
t = 2
\]
Equation 6: \( c + 10 = 10 \)
- Subtract 10 from both sides:
\[
c + 10 - 10 = 10 - 10
\]
\[
c = 0
\]
Equation 7: \( -4 - r = 4 \)
- Add 4 to both sides:
\[
-4 - r + 4 = 4 + 4
\]
\[
-r = 8
\]
- Multiply both sides by -1:
\[
r = -8
\]
Equation 8: \( -y + 3 = 0 \)
- Subtract 3 from both sides:
\[
-y + 3 - 3 = 0 - 3
\]
\[
-y = -3
\]
- Multiply both sides by -1:
\[
y = 3
\]
Equation 9: \( 4 - a = 1 \)
- Subtract 4 from both sides:
\[
4 - a - 4 = 1 - 4
\]
\[
-a = -3
\]
- Multiply both sides by -1:
\[
a = 3
\]
Equation 10: \( z + 3 = 8 \)
- Subtract 3 from both sides:
\[
z + 3 - 3 = 8 - 3
\]
\[
z = 5
\]
Equation 11: \( -2 - x = 5 \)
- Add 2 to both sides:
\[
-2 - x + 2 = 5 + 2
\]
\[
-x = 7
\]
- Multiply both sides by -1:
\[
x = -7
\]
Equation 12: \( b - 32 = 10 \)
- Add 32 to both sides:
\[
b - 32 + 32 = 10 + 32
\]
\[
b = 42
\]
Equation 13: \( -3 + y = 5 \)
- Add 3 to both sides:
\[
-3 + y + 3 = 5 + 3
\]
\[
y = 8
\]
Equation 14: \( z - 5 = -6 \)
- Add 5 to both sides:
\[
z - 5 + 5 = -6 + 5
\]
\[
z = -1
\]
Equation 15: \( n - (-1) = 10 \)
- Simplify the left side:
\[
n + 1 = 10
\]
- Subtract 1 from both sides:
\[
n + 1 - 1 = 10 - 1
\]
\[
n = 9
\]
Equation 16: \( g + 1 = 12 \)
- Subtract 1 from both sides:
\[
g + 1 - 1 = 12 - 1
\]
\[
g = 11
\]
Equation 17: \( -7 + x = 1 \)
- Add 7 to both sides:
\[
-7 + x + 7 = 1 + 7
\]
\[
x = 8
\]
Equation 18: \( c - 13 = 12 \)
- Add 13 to both sides:
\[
c - 13 + 13 = 12 + 13
\]
\[
c = 25
\]
Equation 19: \( -5 - w = 5 \)
- Add 5 to both sides:
\[
-5 - w + 5 = 5 + 5
\]
\[
-w = 10
\]
- Multiply both sides by -1:
\[
w = -10
\]
Equation 20: \( k - 5 = 10 \)
- Add 5 to both sides:
\[
k - 5 + 5 = 10 + 5
\]
\[
k = 15
\]
Equation 21: \( p + 1 = -2 \)
- Subtract 1 from both sides:
\[
p + 1 - 1 = -2 - 1
\]
\[
p = -3
\]
Final Answers:
\[
\boxed{
\begin{aligned}
&y = 2, \quad c = 13, \quad v = 3, \quad k = 17, \quad t = 2, \quad c = 0, \quad r = -8, \quad y = 3, \quad a = 3, \quad z = 5, \\
&x = -7, \quad b = 42, \quad y = 8, \quad z = -1, \quad n = 9, \quad g = 11, \quad x = 8, \quad c = 25, \quad w = -10, \\
&k = 15, \quad p = -3
\end{aligned}
}
\]
Parent Tip: Review the logic above to help your child master the concept of addition of algebraic expressions worksheet.
