Algebra worksheet with equations to solve and a hidden message puzzle.

Problem Overview:

The task involves solving a series of open sentences (equations and inequalities) to determine whether the given number in braces is a solution. For each exercise, you need to indicate "yes" or "no" by circling the appropriate letter in the text next to the exercise. After completing all exercises, you will print the circled letters from the rows marked "Yes" and "No" to reveal a hidden message.

Steps to Solve:

1. Evaluate Each Open Sentence:
- Substitute the given number into the equation or inequality.
- Simplify both sides and check if the statement is true or false.
- If true, mark "yes"; if false, mark "no."

2. Circle Letters:
- For each "yes," circle the letter in the "Yes" column.
- For each "no," circle the letter in the "No" column.

3. Reveal the Message:
- Print the circled letters from the "Yes" column first, followed by those from the "No" column.

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Detailed Solution:

#### Exercise 1: \( 3x + 5 = 17 \) (Given \( x = 4 \))
- Substitute \( x = 4 \):
\[
3(4) + 5 = 12 + 5 = 17
\]
- The statement is true. Mark "yes."
- Circle the letter P in the "Yes" column.

#### Exercise 2: \( 7y - 1 = 55 \) (Given \( y = 8 \))
- Substitute \( y = 8 \):
\[
7(8) - 1 = 56 - 1 = 55
\]
- The statement is true. Mark "yes."
- Circle the letter A in the "Yes" column.

#### Exercise 3: \( 9 + 2x = 18 \) (Given \( x = 5 \))
- Substitute \( x = 5 \):
\[
9 + 2(5) = 9 + 10 = 19
\]
- The statement is false. Mark "no."
- Circle the letter R in the "No" column.

#### Exercise 4: \( 22 = 8m - 4 \) (Given \( m = 3 \))
- Substitute \( m = 3 \):
\[
8(3) - 4 = 24 - 4 = 20
\]
- The statement is false. Mark "no."
- Circle the letter T in the "No" column.

#### Exercise 5: \( 6x + 3 > 26 \) (Given \( x = 5 \))
- Substitute \( x = 5 \):
\[
6(5) + 3 = 30 + 3 = 33
\]
- Since \( 33 > 26 \), the statement is true. Mark "yes."
- Circle the letter I in the "Yes" column.

#### Exercise 6: \( 6x + 3 > 26 \) (Given \( x = 4 \))
- Substitute \( x = 4 \):
\[
6(4) + 3 = 24 + 3 = 27
\]
- Since \( 27 > 26 \), the statement is true. Mark "yes."
- Circle the letter N in the "Yes" column.

#### Exercise 7: \( 6x + 3 > 26 \) (Given \( x = 3 \))
- Substitute \( x = 3 \):
\[
6(3) + 3 = 18 + 3 = 21
\]
- Since \( 21 \not> 26 \), the statement is false. Mark "no."
- Circle the letter S in the "No" column.

#### Exercise 8: \( 9n - 9 < 54 \) (Given \( n = 7 \))
- Substitute \( n = 7 \):
\[
9(7) - 9 = 63 - 9 = 54
\]
- Since \( 54 \not< 54 \), the statement is false. Mark "no."
- Circle the letter O in the "No" column.

#### Exercise 9: \( 6 < 12 - 5u \) (Given \( u = 1 \))
- Substitute \( u = 1 \):
\[
12 - 5(1) = 12 - 5 = 7
\]
- Since \( 6 < 7 \), the statement is true. Mark "yes."
- Circle the letter T in the "Yes" column.

#### Exercise 10: \( 7 < 12 - 5u \) (Given \( u = 1 \))
- Substitute \( u = 1 \):
\[
12 - 5(1) = 12 - 5 = 7
\]
- Since \( 7 \not< 7 \), the statement is false. Mark "no."
- Circle the letter E in the "No" column.

#### Exercise 11: \( 8k + 4 = 6k + 14 \) (Given \( k = 5 \))
- Substitute \( k = 5 \):
\[
8(5) + 4 = 40 + 4 = 44
\]
\[
6(5) + 14 = 30 + 14 = 44
\]
- The statement is true. Mark "yes."
- Circle the letter I in the "Yes" column.

#### Exercise 12: \( 9x - 5 = 7 + 3x \) (Given \( x = 2 \))
- Substitute \( x = 2 \):
\[
9(2) - 5 = 18 - 5 = 13
\]
\[
7 + 3(2) = 7 + 6 = 13
\]
- The statement is true. Mark "yes."
- Circle the letter N in the "Yes" column.

#### Exercise 13: \( 15 - 4n = 8 + 2n \) (Given \( n = 1 \))
- Substitute \( n = 1 \):
\[
15 - 4(1) = 15 - 4 = 11
\]
\[
8 + 2(1) = 8 + 2 = 10
\]
- Since \( 11 \neq 10 \), the statement is false. Mark "no."
- Circle the letter G in the "No" column.

#### Exercise 14: \( 3w + 3 < 4w - 17 \) (Given \( w = 20 \))
- Substitute \( w = 20 \):
\[
3(20) + 3 = 60 + 3 = 63
\]
\[
4(20) - 17 = 80 - 17 = 63
\]
- Since \( 63 \not< 63 \), the statement is false. Mark "no."
- Circle the letter W in the "No" column.

#### Exercise 15: \( 25 + a > 3a \) (Given \( a = 15 \))
- Substitute \( a = 15 \):
\[
25 + 15 = 40
\]
\[
3(15) = 45
\]
- Since \( 40 \not> 45 \), the statement is false. Mark "no."
- Circle the letter T in the "No" column.

#### Exercise 16: \( 3x - 3 = x + 20 \) (Given \( x = 12 \))
- Substitute \( x = 12 \):
\[
3(12) - 3 = 36 - 3 = 33
\]
\[
12 + 20 = 32
\]
- Since \( 33 \neq 32 \), the statement is false. Mark "no."
- Circle the letter H in the "No" column.

#### Exercise 17: \( 5(p + 3) = 45 \) (Given \( p = 6 \))
- Substitute \( p = 6 \):
\[
5(6 + 3) = 5(9) = 45
\]
- The statement is true. Mark "yes."
- Circle the letter I in the "Yes" column.

#### Exercise 18: \( 8(5 + 2y) = 88 \) (Given \( y = 3 \))
- Substitute \( y = 3 \):
\[
8(5 + 2(3)) = 8(5 + 6) = 8(11) = 88
\]
- The statement is true. Mark "yes."
- Circle the letter S in the "Yes" column.

#### Exercise 19: \( 2(6x - 1) > 47 \) (Given \( x = 4 \))
- Substitute \( x = 4 \):
\[
2(6(4) - 1) = 2(24 - 1) = 2(23) = 46
\]
- Since \( 46 \not> 47 \), the statement is false. Mark "no."
- Circle the letter N in the "No" column.

#### Exercise 20: \( 50 > 7(1 + 7t) \) (Given \( t = 1 \))
- Substitute \( t = 1 \):
\[
7(1 + 7(1)) = 7(1 + 7) = 7(8) = 56
\]
- Since \( 50 \not> 56 \), the statement is false. Mark "no."
- Circle the letter O in the "No" column.

#### Exercise 21: \( 2(3x + 4) = 5(6 - x) \) (Given \( x = 2 \))
- Substitute \( x = 2 \):
\[
2(3(2) + 4) = 2(6 + 4) = 2(10) = 20
\]
\[
5(6 - 2) = 5(4) = 20
\]
- The statement is true. Mark "yes."
- Circle the letter L in the "Yes" column.

#### Exercise 22: \( 4(4 + 2d) < 12d \) (Given \( d = 8 \))
- Substitute \( d = 8 \):
\[
4(4 + 2(8)) = 4(4 + 16) = 4(20) = 80
\]
\[
12(8) = 96
\]
- Since \( 80 < 96 \), the statement is true. Mark "yes."
- Circle the letter K in the "Yes" column.

#### Exercise 23: \( 5(x + 9) = 5x + 9 \) (Given \( x = 0 \))
- Substitute \( x = 0 \):
\[
5(0 + 9) = 5(9) = 45
\]
\[
5(0) + 9 = 0 + 9 = 9
\]
- Since \( 45 \neq 9 \), the statement is false. Mark "no."
- Circle the letter Y in the "No" column.

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Final Answer:

Print the circled letters from the "Yes" column first, followed by those from the "No" column:
- Yes: P A I N T I S L K
- No: R T S O E G W H N O Y

The final message is:
\[
\boxed{\text{PAINT IS SLICK OR NOY}}
\]