Combining Like Terms and Solving Simple Linear Equations (A) - Free Printable

The provided image contains a worksheet titled "Simplifying and Solving Equations (A) Answers." The task involves solving each equation to determine the value of the unknown variable. Below, I will explain the solution process for a few selected equations as examples. If you need detailed solutions for specific equations, please let me know!

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General Approach to Solving Linear Equations

1. Simplify both sides: Expand any parentheses and combine like terms.
2. Isolate the variable: Move all terms involving the variable to one side of the equation and all constant terms to the other side.
3. Solve for the variable: Divide or multiply as needed to isolate the variable completely.

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Selected Examples

#### Equation 1: \( 2(3 - h) - 6 = -5h \)
1. Expand the parentheses:
\[
2(3 - h) - 6 = -5h
\]
\[
6 - 2h - 6 = -5h
\]
2. Simplify:
\[
-2h = -5h
\]
3. Add \( 5h \) to both sides:
\[
-2h + 5h = 0
\]
\[
3h = 0
\]
4. Solve for \( h \):
\[
h = 0
\]

#### Equation 2: \( 7 + 9d = 7d + 3 \)
1. Subtract \( 7d \) from both sides:
\[
7 + 9d - 7d = 7d + 3 - 7d
\]
\[
7 + 2d = 3
\]
2. Subtract 7 from both sides:
\[
7 + 2d - 7 = 3 - 7
\]
\[
2d = -4
\]
3. Divide by 2:
\[
d = -2
\]

#### Equation 3: \( -2(4 + 3y) = -2(4 + y) \)
1. Expand both sides:
\[
-2(4 + 3y) = -2(4 + y)
\]
\[
-8 - 6y = -8 - 2y
\]
2. Add 8 to both sides:
\[
-8 - 6y + 8 = -8 - 2y + 8
\]
\[
-6y = -2y
\]
3. Add \( 2y \) to both sides:
\[
-6y + 2y = -2y + 2y
\]
\[
-4y = 0
\]
4. Solve for \( y \):
\[
y = 0
\]

#### Equation 4: \( -7 + 4c = 7c + 6 \)
1. Subtract \( 4c \) from both sides:
\[
-7 + 4c - 4c = 7c + 6 - 4c
\]
\[
-7 = 3c + 6
\]
2. Subtract 6 from both sides:
\[
-7 - 6 = 3c + 6 - 6
\]
\[
-13 = 3c
\]
3. Divide by 3:
\[
c = -\frac{13}{3}
\]

#### Equation 5: \( 5(1 + s) = -9s + 6 \)
1. Expand the left side:
\[
5(1 + s) = -9s + 6
\]
\[
5 + 5s = -9s + 6
\]
2. Add \( 9s \) to both sides:
\[
5 + 5s + 9s = -9s + 6 + 9s
\]
\[
5 + 14s = 6
\]
3. Subtract 5 from both sides:
\[
5 + 14s - 5 = 6 - 5
\]
\[
14s = 1
\]
4. Divide by 14:
\[
s = \frac{1}{14}
\]

#### Equation 6: \( 3 + v = 2(2v - 1) \)
1. Expand the right side:
\[
3 + v = 2(2v - 1)
\]
\[
3 + v = 4v - 2
\]
2. Subtract \( v \) from both sides:
\[
3 + v - v = 4v - 2 - v
\]
\[
3 = 3v - 2
\]
3. Add 2 to both sides:
\[
3 + 2 = 3v - 2 + 2
\]
\[
5 = 3v
\]
4. Divide by 3:
\[
v = \frac{5}{3}
\]

#### Equation 7: \( -2 - 4w = 7w - 8 \)
1. Add \( 4w \) to both sides:
\[
-2 - 4w + 4w = 7w - 8 + 4w
\]
\[
-2 = 11w - 8
\]
2. Add 8 to both sides:
\[
-2 + 8 = 11w - 8 + 8
\]
\[
6 = 11w
\]
3. Divide by 11:
\[
w = \frac{6}{11}
\]

#### Equation 8: \( -6(1 - m) = 9 - 2m \)
1. Expand the left side:
\[
-6(1 - m) = 9 - 2m
\]
\[
-6 + 6m = 9 - 2m
\]
2. Add \( 2m \) to both sides:
\[
-6 + 6m + 2m = 9 - 2m + 2m
\]
\[
-6 + 8m = 9
\]
3. Add 6 to both sides:
\[
-6 + 8m + 6 = 9 + 6
\]
\[
8m = 15
\]
4. Divide by 8:
\[
m = \frac{15}{8}
\]

#### Equation 9: \( -2q - 3 = -2(2q + 1) \)
1. Expand the right side:
\[
-2q - 3 = -2(2q + 1)
\]
\[
-2q - 3 = -4q - 2
\]
2. Add \( 4q \) to both sides:
\[
-2q - 3 + 4q = -4q - 2 + 4q
\]
\[
2q - 3 = -2
\]
3. Add 3 to both sides:
\[
2q - 3 + 3 = -2 + 3
\]
\[
2q = 1
\]
4. Divide by 2:
\[
q = \frac{1}{2}
\]

#### Equation 10: \( 6n + 7 = 2n + 5 \)
1. Subtract \( 2n \) from both sides:
\[
6n + 7 - 2n = 2n + 5 - 2n
\]
\[
4n + 7 = 5
\]
2. Subtract 7 from both sides:
\[
4n + 7 - 7 = 5 - 7
\]
\[
4n = -2
\]
3. Divide by 4:
\[
n = -\frac{1}{2}
\]

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Final Answer

The solutions to the equations are already provided in the image. Here they are summarized:

1. \( h = 0 \)
2. \( d = -2 \)
3. \( y = 0 \)
4. \( c = -\frac{13}{3} \)
5. \( s = \frac{1}{14} \)
6. \( v = \frac{5}{3} \)
7. \( w = \frac{6}{11} \)
8. \( m = \frac{15}{8} \)
9. \( q = \frac{1}{2} \)
10. \( n = -\frac{1}{2} \)
11. \( x = -\frac{5}{11} \)
12. \( p = -1 \)
13. \( g = 1 \)
14. \( b = -4 \)
15. \( z = 5 \)
16. \( a = \frac{5}{7} \)
17. \( t = -\frac{4}{13} \)
18. \( f = -\frac{2}{3} \)
19. \( r = -1 \)
20. \( k = \frac{1}{13} \)

\boxed{\text{See above for detailed solutions.}}