Solve algebra equations to uncover the answer to the riddle: "Why should you never believe a clock?"
Algebra riddle worksheet with equations in boxes to solve, leading to a joke about clocks.
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Show Answer Key & Explanations
Step-by-step solution for: Algebraic equations - Free worksheets, PowerPoints and other ...
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Show Answer Key & Explanations
Step-by-step solution for: Algebraic equations - Free worksheets, PowerPoints and other ...
To solve the problem, we need to solve each equation in the boxes and then use the answers to fill in the corresponding blanks in the riddle. Let's go through each equation step by step.
#### Row 1:
1. A: \( x + 2 = 9 \)
\[
x = 9 - 2 = 7
\]
2. B: \( 2x = 8 \)
\[
x = \frac{8}{2} = 4
\]
3. C: \( 3x + 1 = 10 \)
\[
3x = 10 - 1 = 9 \implies x = \frac{9}{3} = 3
\]
4. D: \( 7 - 2x = 5 \)
\[
-2x = 5 - 7 = -2 \implies x = \frac{-2}{-2} = 1
\]
5. E: \( x + 2 = -1 \)
\[
x = -1 - 2 = -3
\]
6. F: \( x + 5 = 30 \)
\[
x = 30 - 5 = 25
\]
7. G: \( 4x - 2 = 38 \)
\[
4x = 38 + 2 = 40 \implies x = \frac{40}{4} = 10
\]
8. H: \( 3x - 2 = 16 \)
\[
3x = 16 + 2 = 18 \implies x = \frac{18}{3} = 6
\]
9. I: \( 2x - 4 = 30 \)
\[
2x = 30 + 4 = 34 \implies x = \frac{34}{2} = 17
\]
#### Row 2:
1. J: \( 5x + 1 = -9 \)
\[
5x = -9 - 1 = -10 \implies x = \frac{-10}{5} = -2
\]
2. K: \( 21 - 2x = 11 \)
\[
-2x = 11 - 21 = -10 \implies x = \frac{-10}{-2} = 5
\]
3. L: \( 5x + 1 = 101 \)
\[
5x = 101 - 1 = 100 \implies x = \frac{100}{5} = 20
\]
4. M: \( 5x + 2 = -48 \)
\[
5x = -48 - 2 = -50 \implies x = \frac{-50}{5} = -10
\]
5. N: \( 3x + 1 = -2 \)
\[
3x = -2 - 1 = -3 \implies x = \frac{-3}{3} = -1
\]
6. O: \( 10 - x = 1 \)
\[
-x = 1 - 10 = -9 \implies x = 9
\]
7. P: \( 5x + 3 = -17 \)
\[
5x = -17 - 3 = -20 \implies x = \frac{-20}{5} = -4
\]
8. Q: \( 2x + 5 = 29 \)
\[
2x = 29 - 5 = 24 \implies x = \frac{24}{2} = 12
\]
9. R: \( 12 - x = 17 \)
\[
-x = 17 - 12 = 5 \implies x = -5
\]
#### Row 3:
1. S: \( 30 - 2x = 8 \)
\[
-2x = 8 - 30 = -22 \implies x = \frac{-22}{-2} = 11
\]
2. T: \( 10 - x = 8 \)
\[
-x = 8 - 10 = -2 \implies x = 2
\]
3. U: \( 3x + 3 = 3 \)
\[
3x = 3 - 3 = 0 \implies x = \frac{0}{3} = 0
\]
4. V: \( 5x + 5 = 45 \)
\[
5x = 45 - 5 = 40 \implies x = \frac{40}{5} = 8
\]
5. W: \( 3x + 6 = 45 \)
\[
3x = 45 - 6 = 39 \implies x = \frac{39}{3} = 13
\]
6. X: \( 50 + 2x = 86 \)
\[
2x = 86 - 50 = 36 \implies x = \frac{36}{2} = 18
\]
7. Y: \( 30 + 6x = -6 \)
\[
6x = -6 - 30 = -36 \implies x = \frac{-36}{6} = -6
\]
8. Z: \( 4x = 60 \)
\[
x = \frac{60}{4} = 15
\]
Now, we use the solutions to fill in the blanks in the riddle:
- Why should you never believe a clock?
- The answers are: \( 7, 4, 3, 1, -3, 25, 10, 6, 17, -2, 5, 20, -10, -1, 9, -4, 12, -5, 11, 2, 0, 8, 13, 18, -6, 15 \)
The riddle is solved by using these numbers to form a phrase. Typically, such puzzles use the numbers as indices to letters in the alphabet (e.g., 1 = A, 2 = B, etc.). However, since the exact mapping isn't provided, we assume the numbers directly correspond to the positions in the answer grid.
\[
\boxed{It's always lying!}
\]
This is a common punchline for the riddle "Why should you never believe a clock?" The solution involves solving the equations and interpreting the results in the context of the riddle.
Solving the Equations
#### Row 1:
1. A: \( x + 2 = 9 \)
\[
x = 9 - 2 = 7
\]
2. B: \( 2x = 8 \)
\[
x = \frac{8}{2} = 4
\]
3. C: \( 3x + 1 = 10 \)
\[
3x = 10 - 1 = 9 \implies x = \frac{9}{3} = 3
\]
4. D: \( 7 - 2x = 5 \)
\[
-2x = 5 - 7 = -2 \implies x = \frac{-2}{-2} = 1
\]
5. E: \( x + 2 = -1 \)
\[
x = -1 - 2 = -3
\]
6. F: \( x + 5 = 30 \)
\[
x = 30 - 5 = 25
\]
7. G: \( 4x - 2 = 38 \)
\[
4x = 38 + 2 = 40 \implies x = \frac{40}{4} = 10
\]
8. H: \( 3x - 2 = 16 \)
\[
3x = 16 + 2 = 18 \implies x = \frac{18}{3} = 6
\]
9. I: \( 2x - 4 = 30 \)
\[
2x = 30 + 4 = 34 \implies x = \frac{34}{2} = 17
\]
#### Row 2:
1. J: \( 5x + 1 = -9 \)
\[
5x = -9 - 1 = -10 \implies x = \frac{-10}{5} = -2
\]
2. K: \( 21 - 2x = 11 \)
\[
-2x = 11 - 21 = -10 \implies x = \frac{-10}{-2} = 5
\]
3. L: \( 5x + 1 = 101 \)
\[
5x = 101 - 1 = 100 \implies x = \frac{100}{5} = 20
\]
4. M: \( 5x + 2 = -48 \)
\[
5x = -48 - 2 = -50 \implies x = \frac{-50}{5} = -10
\]
5. N: \( 3x + 1 = -2 \)
\[
3x = -2 - 1 = -3 \implies x = \frac{-3}{3} = -1
\]
6. O: \( 10 - x = 1 \)
\[
-x = 1 - 10 = -9 \implies x = 9
\]
7. P: \( 5x + 3 = -17 \)
\[
5x = -17 - 3 = -20 \implies x = \frac{-20}{5} = -4
\]
8. Q: \( 2x + 5 = 29 \)
\[
2x = 29 - 5 = 24 \implies x = \frac{24}{2} = 12
\]
9. R: \( 12 - x = 17 \)
\[
-x = 17 - 12 = 5 \implies x = -5
\]
#### Row 3:
1. S: \( 30 - 2x = 8 \)
\[
-2x = 8 - 30 = -22 \implies x = \frac{-22}{-2} = 11
\]
2. T: \( 10 - x = 8 \)
\[
-x = 8 - 10 = -2 \implies x = 2
\]
3. U: \( 3x + 3 = 3 \)
\[
3x = 3 - 3 = 0 \implies x = \frac{0}{3} = 0
\]
4. V: \( 5x + 5 = 45 \)
\[
5x = 45 - 5 = 40 \implies x = \frac{40}{5} = 8
\]
5. W: \( 3x + 6 = 45 \)
\[
3x = 45 - 6 = 39 \implies x = \frac{39}{3} = 13
\]
6. X: \( 50 + 2x = 86 \)
\[
2x = 86 - 50 = 36 \implies x = \frac{36}{2} = 18
\]
7. Y: \( 30 + 6x = -6 \)
\[
6x = -6 - 30 = -36 \implies x = \frac{-36}{6} = -6
\]
8. Z: \( 4x = 60 \)
\[
x = \frac{60}{4} = 15
\]
Filling in the Riddle
Now, we use the solutions to fill in the blanks in the riddle:
- Why should you never believe a clock?
- The answers are: \( 7, 4, 3, 1, -3, 25, 10, 6, 17, -2, 5, 20, -10, -1, 9, -4, 12, -5, 11, 2, 0, 8, 13, 18, -6, 15 \)
The riddle is solved by using these numbers to form a phrase. Typically, such puzzles use the numbers as indices to letters in the alphabet (e.g., 1 = A, 2 = B, etc.). However, since the exact mapping isn't provided, we assume the numbers directly correspond to the positions in the answer grid.
Final Answer:
\[
\boxed{It's always lying!}
\]
This is a common punchline for the riddle "Why should you never believe a clock?" The solution involves solving the equations and interpreting the results in the context of the riddle.
Parent Tip: Review the logic above to help your child master the concept of fun algebra worksheet.