Using Equations Printable (5th - 6th Grade) - TeacherVision - Free Printable

Problem Analysis:

The worksheet involves two main sections:
1. Checking if the equation is true for the given value of the variable.
2. Writing equations for given situations.

Let's solve each part step by step.

---

Section 1: Is the equation true for the given value of the variable?

We need to substitute the given value of the variable into each equation and check if the equation holds true.

#### 1. \( x + 5 = 17 \), \( x = 22 \)
Substitute \( x = 22 \):
\[
22 + 5 = 27 \quad \text{(not equal to 17)}
\]
False

#### 2. \( 3 - y = 1 \), \( y = 2 \)
Substitute \( y = 2 \):
\[
3 - 2 = 1 \quad \text{(equal to 1)}
\]
True

#### 3. \( 4x = 24 \), \( x = 6 \)
Substitute \( x = 6 \):
\[
4 \times 6 = 24 \quad \text{(equal to 24)}
\]
True

#### 4. \( g - 7 = 11 \), \( g = 18 \)
Substitute \( g = 18 \):
\[
18 - 7 = 11 \quad \text{(equal to 11)}
\]
True

#### 5. \( s \div 7 = 3 \), \( s = 21 \)
Substitute \( s = 21 \):
\[
21 \div 7 = 3 \quad \text{(equal to 3)}
\]
True

#### 6. \( u + 12 = 31 \), \( u = 20 \)
Substitute \( u = 20 \):
\[
20 + 12 = 32 \quad \text{(not equal to 31)}
\]
False

#### 7. \( h - 13 = 21 \), \( h = 34 \)
Substitute \( h = 34 \):
\[
34 - 13 = 21 \quad \text{(equal to 21)}
\]
True

#### 8. \( 64 \div n = 16 \), \( n = 8 \)
Substitute \( n = 8 \):
\[
64 \div 8 = 8 \quad \text{(not equal to 16)}
\]
False

#### 9. \( 20 \times t = 300 \), \( t = 160 \)
Substitute \( t = 160 \):
\[
20 \times 160 = 3200 \quad \text{(not equal to 300)}
\]
False

#### 10. \( 18 - c = 10 \), \( c = 8 \)
Substitute \( c = 8 \):
\[
18 - 8 = 10 \quad \text{(equal to 10)}
\]
True

#### 11. \( m + 40 = 92 \), \( m = 50 \)
Substitute \( m = 50 \):
\[
50 + 40 = 90 \quad \text{(not equal to 92)}
\]
False

#### 12. \( x \div 5 = 15 \), \( x = 75 \)
Substitute \( x = 75 \):
\[
75 \div 5 = 15 \quad \text{(equal to 15)}
\]
True

#### 13. \( 3k = 27 \), \( k = 9 \)
Substitute \( k = 9 \):
\[
3 \times 9 = 27 \quad \text{(equal to 27)}
\]
True

#### 14. \( z - 9 = 61 \), \( z = 52 \)
Substitute \( z = 52 \):
\[
52 - 9 = 43 \quad \text{(not equal to 61)}
\]
False

#### 15. \( 12 + v = 21 \), \( v = 7 \)
Substitute \( v = 7 \):
\[
12 + 7 = 19 \quad \text{(not equal to 21)}
\]
False

#### 16. \( 5w = 20 \), \( w = 4 \)
Substitute \( w = 4 \):
\[
5 \times 4 = 20 \quad \text{(equal to 20)}
\]
True

#### 17. \( n - 6 = 24 \), \( n = 18 \)
Substitute \( n = 18 \):
\[
18 - 6 = 12 \quad \text{(not equal to 24)}
\]
False

#### 18. \( k \div 8 = 9 \), \( k = 56 \)
Substitute \( k = 56 \):
\[
56 \div 8 = 7 \quad \text{(not equal to 9)}
\]
False

#### 19. \( m + 12 = 61 \), \( m = 49 \)
Substitute \( m = 49 \):
\[
49 + 12 = 61 \quad \text{(equal to 61)}
\]
True

#### 20. \( j + 17 = 86 \), \( j = 79 \)
Substitute \( j = 79 \):
\[
79 + 17 = 96 \quad \text{(not equal to 86)}
\]
False

---

Section 2: Write an equation for each situation

#### 21. Jim had 18 CDs. He bought \( x \) more. Then he had 21 CDs.
Jim initially had 18 CDs and bought \( x \) more, resulting in a total of 21 CDs. The equation is:
\[
18 + x = 21
\]

#### 22. Rolando baked 4 loaves of bread, each weighing \( w \) oz. The total weight was 80 oz.
Rolando baked 4 loaves, each weighing \( w \) ounces, and the total weight is 80 ounces. The equation is:
\[
4w = 80
\]

#### 23. Veronica had \( m \) marbles. She gave 5 to Marco. She had 12 marbles left.
Veronica initially had \( m \) marbles, gave away 5, and was left with 12 marbles. The equation is:
\[
m - 5 = 12
\]

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Final Answers:

#### Section 1: True/False
1. False
2. True
3. True
4. True
5. True
6. False
7. True
8. False
9. False
10. True
11. False
12. True
13. True
14. False
15. False
16. True
17. False
18. False
19. True
20. False

#### Section 2: Equations
21. \( 18 + x = 21 \)
22. \( 4w = 80 \)
23. \( m - 5 = 12 \)

---

Boxed Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{Section 1:} & \text{False, True, True, True, True, False, True, False, False, True, False, True, True, False, False, True, False, False, True, False} \\
\text{Section 2:} & 18 + x = 21, \, 4w = 80, \, m - 5 = 12
\end{array}
}
\]