Let's solve each equation step by step and match the answers to find the letters corresponding to the numbers.
**Set 1:**
E. \(- 3 - 3x = - 4( 2x + 7) \)
\[-3 - 3x = -8x - 28 \\
-3 + 28 = -8x + 3x \\
25 = -5x \\
x = -5\]
A. \(8x + 3 = 8x + 27\)
\[8x + 3 = 8x + 27 \\
3 \neq 27 \\
\text{No solution}\]
O. \(2( x - 4) = 7 - 3x\)
\[2x - 8 = 7 - 3x \\
2x + 3x = 7 + 8 \\
5x = 15 \\
x = 3\]
8. \(- 3 - 6( x - 7) = 42 - 6x\)
\[-3 - 6x + 42 = 42 - 6x \\
39 = 42 \\
\text{No solution}\]
5. \(6( 1 - 3x) = - 36 - 4x\)
\[6 - 18x = -36 - 4x \\
6 + 36 = 18x - 4x \\
42 = 14x \\
x = 3\]
10. \(5 + 4( x - 1) = 2x - 9\)
\[5 + 4x - 4 = 2x - 9 \\
4x + 1 = 2x - 9 \\
4x - 2x = -9 - 1 \\
2x = -10 \\
x = -5\]
Matching results for Set 1:

• E matches 10 (both \(x = - 5\))
• O matches 5 (both \(x = 3\))
• *Set 2:**
  O. \(6( x - 6) + 4 = - 32 + 6x\)
  \[6x - 36 + 4 = -32 + 6x \\
  6x - 32 = 6x - 32 \\
  \text{Infinite solutions}\]
  N. \(- 2x - 40 = 8( 1 - x) \)
  \(undefined\)-2x - 40 = 8 - 8x \\
• 2x + 8x = 8 + 40 \\
  6x = 48 \\
  x = 8\(\[T. $- 9 - 8x = - 2( 7 + 4x) \]\(- 9 - 8x = - 14 - 8x \\ \)
• 9 \neq -14 \\
  \text{No solution}\)\[$

1. $2(x - 3) = -2 + 2x$
   \]2x - 6 = -2 + 2x \\
   2x - 2x = -2 + 6 \\
   0 = 4 \\
   \text{No solution}\[
2. $-12 + 6x = 6 + 5(x - 2)$
   \]\[-12 + 6x = 6 + 5x - 10 \\

-12 + 6x = -4 + 5x \\
6x - 5x = -4 + 12 \\
x = 8\]2. \(\(- 17 + 5x = 5( x - 5) + 8\)\[- 17 + 5x = 5x - 25 + 8 \\ \)
-17 = -17 \\
\text{Infinite solutions}\]\[
Matching results for Set 2:

• N matches 6 (both $x = 8$)
• *Set 3:**
  C. $2x + 8 = 2(x + 4)$
  \]2x + 8 = 2x + 8 \\
  \text{Infinite solutions}\[
  T. $x - 20 = 5(7x - 4)$
  \]\[x - 20 = 35x - 20 \\
  x - 35x = 0 \\
• 34x = 0 \\
  x = 0\]M. \(\(- 4( 8 + 7x) = - 10 - 6x\)\[- 32 - 28x = - 10 - 6x \\ \)
• 32 + 10 = 28x - 6x \\
• 22 = 22x \\
  x = -1\]\[

1. $7(1 - 2x) = 4 - 2x$
   \]7 - 14x = 4 - 2x \\
   7 - 4 = -2x + 14x \\
   3 = 12x \\
   x = \frac{1}{4}\[
2. $8 - 8(1 + 3x) = 23 - x$
   \]\[8 - 8 - 24x = 23 - x \\

-24x = 23 - x \\
-24x + x = 23 \\
-23x = 23 \\
x = -1\]\[

1. $-(5x + 6) = -6 - 6x$
   \]\[-5x - 6 = -6 - 6x \\

-5x + 6x = -6 + 6 \\
x = 0\]\[
Matching results for Set 3:

• T matches 1 (both $x = 0$)
• M matches 4 (both $x = -1$)
• *Set 4:**
  R. $28 + 8x = 8(x + 3) + 2$
  \]28 + 8x = 8x + 24 + 2 \\
  28 + 8x = 8x + 26 \\
  28 = 26 \\
  \text{No solution}\[
  M. $-35 - 7x = -7(x + 5)$
  \]\[-35 - 7x = -7x - 35 \\
• 35 = -35 \\
  \text{Infinite solutions}\]\[

1. $3(x - 7) = -21 + 3x$
   \]3x - 21 = -21 + 3x \\
   3x - 3x = -21 + 21 \\
   0 = 0 \\
   \text{Infinite solutions}\[
2. $3x = 3(x - 1)$
   \]3x = 3x - 3 \\
   3 = 0 \\
   \text{No solution}\(\)
   Matching results for Set 4:

• No matching results for Set 4 due to infinite solutions or no solutions.
• *Final Answer:**

1. T
2. O
3. R
4. M
5. O
6. N
7. C
8. E
9. T
10. E
11. M
    The letters corresponding to the numbers spell out: "TOMATO". So, the answer to the riddle "WHAT DO YOU CALL A POTATO WHO READS THE NEWS?" is "TOMATO".

Supplemental Knowledge

Solving linear equations involves finding the value of the variable that makes the equation true. This typically requires isolating the variable on one side of the equation through a series of algebraic steps, such as combining like terms, using the distributive property, and performing inverse operations.

Real-Life Connections

Imagine you're budgeting for a project. You have a fixed amount to spend and various costs to consider. Solving linear equations can help you determine how much you can allocate to each expense while staying within your budget. This practical application shows how algebra is used in financial planning and decision-making.

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