Solve multi-step equations to crack the code and discover the joke about a rock group.

Explanation:
We need to solve each multi-step equation, find the value of $ x $, and then match that number to the code at the bottom. Each letter (T, O, S, N, U, H, E, C, M, R) corresponds to one equation. After solving all equations, we’ll look for those solution values in the code line and write the corresponding letters in order to reveal the joke.

Let’s solve each equation one by one.

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1. T: $ -2(3 + 5x) = 2x + 6 $
Expand left side:
$ -2 \cdot 3 = -6 $, $ -2 \cdot 5x = -10x $ → $ -6 - 10x = 2x + 6 $
Add $ 10x $ to both sides:
$ -6 = 12x + 6 $
Subtract 6:
$ -12 = 12x $
Divide by 12:
$ x = -1 $

✔ T = –1

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2. O: $ 10x - 3 = 2x - 8 + 7x $
Simplify right side: $ 2x + 7x = 9x $, so $ 9x - 8 $
Equation: $ 10x - 3 = 9x - 8 $
Subtract $ 9x $: $ x - 3 = -8 $
Add 3: $ x = -5 $

✔ O = –5

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3. S: $ -4x - 8 + 6x = 16 - 6x $
Simplify left: $ (-4x + 6x) = 2x $, so $ 2x - 8 = 16 - 6x $
Add $ 6x $: $ 8x - 8 = 16 $
Add 8: $ 8x = 24 $
Divide: $ x = 3 $

✔ S = 3

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4. N: $ 12x + 3(2 - 5x) = 16 - 8x $
Expand: $ 3(2 - 5x) = 6 - 15x $
So left side: $ 12x + 6 - 15x = -3x + 6 $
Equation: $ -3x + 6 = 16 - 8x $
Add $ 8x $: $ 5x + 6 = 16 $
Subtract 6: $ 5x = 10 $
Divide: $ x = 2 $

✔ N = 2

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5. U: $ 9(2 - x) + 11 = 8 - 12x $
Expand: $ 9 \cdot 2 = 18 $, $ 9 \cdot (-x) = -9x $ → $ 18 - 9x + 11 = 29 - 9x $
Equation: $ 29 - 9x = 8 - 12x $
Add $ 12x $: $ 29 + 3x = 8 $
Subtract 29: $ 3x = -21 $
Divide: $ x = -7 $

✔ U = –7

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6. H: $ -12 = 5(6 - 3x) + 8x $
Expand: $ 5(6 - 3x) = 30 - 15x $
So right side: $ 30 - 15x + 8x = 30 - 7x $
Equation: $ -12 = 30 - 7x $
Subtract 30: $ -42 = -7x $
Divide: $ x = 6 $

✔ H = 6

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7. E: $ -8x - 14 = 5(2 - x) $
Expand right: $ 5(2 - x) = 10 - 5x $
Equation: $ -8x - 14 = 10 - 5x $
Add $ 8x $: $ -14 = 10 + 3x $
Subtract 10: $ -24 = 3x $
Divide: $ x = -8 $

✔ E = –8

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8. C: $ 6(x + 1) - 2 = -3x - 14 $
Expand left: $ 6x + 6 - 2 = 6x + 4 $
Equation: $ 6x + 4 = -3x - 14 $
Add $ 3x $: $ 9x + 4 = -14 $
Subtract 4: $ 9x = -18 $
Divide: $ x = -2 $

Wait — but –2 is not in the code list! Let’s double-check.

Code numbers are:
4, –5, –7, 2, –1, 9, –7, 3, 6, 4, –5, 9, –8

We have:
T = –1
O = –5
S = 3
N = 2
U = –7
H = 6
E = –8
C = ?
M = ?
R = ?

Hold on — maybe I made a mistake. Let’s re-solve C carefully:

$ 6(x+1) - 2 = -3x -14 $
→ $ 6x + 6 - 2 = -3x -14 $
→ $ 6x + 4 = -3x -14 $
Add $ 3x $: $ 9x + 4 = -14 $
Subtract 4: $ 9x = -18 $
→ $ x = -2 $

Yes, correct. But –2 is *not* in the code line. The problem says: “Not every letter will be used in the code.” So maybe C is not needed for the final answer. Let’s keep going — maybe only some letters appear in the code.

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9. M: $ 4x + 8(3 - 2x) = -24 $
Expand: $ 8(3 - 2x) = 24 - 16x $
Left side: $ 4x + 24 - 16x = -12x + 24 $
Equation: $ -12x + 24 = -24 $
Subtract 24: $ -12x = -48 $
Divide: $ x = 4 $

✔ M = 4

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10. R: $ -10x + 6 = 3 - 3(2x + 11) $
Expand right: $ 3(2x + 11) = 6x + 33 $, so $ -3(2x + 11) = -6x - 33 $
Right side total: $ 3 - 6x - 33 = -6x - 30 $
Equation: $ -10x + 6 = -6x - 30 $
Add $ 10x $: $ 6 = 4x - 30 $
Add 30: $ 36 = 4x $
Divide: $ x = 9 $

✔ R = 9

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Now collect all solutions:
- T = –1
- O = –5
- S = 3
- N = 2
- U = –7
- H = 6
- E = –8
- C = –2 *(not in code)*
- M = 4
- R = 9

Now look at the code line:

`_ 4 _ –5 _ –7 _ 2 _ –1 _ 9 _ –7 _ 3 _ 6 _ 4 _ –5 _ 9 _ –8 !`

Let’s number positions (1 to 15 blanks):

Positions with numbers:
1: 4
2: –5
3: –7
4: 2
5: –1
6: 9
7: –7
8: 3
9: 6
10: 4
11: –5
12: 9
13: –8

We need to fill blanks with letters whose solution matches the number above.

So:
- Where we see 4 → which letter has x = 4? → M
- –5 → O
- –7 → U
- 2 → N
- –1 → T
- 9 → R
- 3 → S
- 6 → H
- –8 → E

Now map in order of the code blanks:

Blank 1: 4 → M
Blank 2: –5 → O
Blank 3: –7 → U
Blank 4: 2 → N
Blank 5: –1 → T
Blank 6: 9 → R
Blank 7: –7 → U
Blank 8: 3 → S
Blank 9: 6 → H
Blank 10: 4 → M
Blank 11: –5 → O
Blank 12: 9 → R
Blank 13: –8 → E

So the letters in order:
M O U N T R U S H M O R E

Wait — that’s “MOUNT RUSHMORE”? But the question asks:
What rock group has four members that can’t sing or play instruments?

Hmm… maybe we misread the code spacing.

Let me count the underscores and numbers again from the image description:

The code line is:
`_ 4 _ –5 _ –7 _ 2 _ –1 _ 9 _ –7 _ 3 _ 6 _ 4 _ –5 _ 9 _ –8 !`

That’s 13 numbers, and 14 underscores? Actually, pattern is: underscore, number, underscore, number, … ending with “!”
So likely 13 blanks (one before each number), but usually in these puzzles, the numbers are under the blanks — i.e., each blank corresponds to a number directly below it.

Looking again: the line shows:
_ 4 _ –5 _ –7 _ 2 _ –1 _ 9 _ –7 _ 3 _ 6 _ 4 _ –5 _ 9 _ –8 !

So there are 14 underscores (blanks), and 13 numbers — but likely the first blank is before 4, then after 4 is next blank, etc. Standard format: blank, number, blank, number… ending with !.

But more reliably: the numbers listed are the solutions, and we place the letter *above* the number that matches its solution.

So read the code as a sequence of numbers, and for each number, write the letter whose equation solves to that number.

Sequence of numbers:
4, –5, –7, 2, –1, 9, –7, 3, 6, 4, –5, 9, –8

Now convert:
4 → M
–5 → O
–7 → U
2 → N
–1 → T
9 → R
–7 → U
3 → S
6 → H
4 → M
–5 → O
9 → R
–8 → E

So: M O U N T R U S H M O R E

That spells MOUNT RUSHMORE — but the question asks for a *rock group* with four members that can’t sing or play instruments.

Wait — maybe it's a pun: “The Rolling Stones”? No, they do play.

Hold on — maybe we made a mistake with one equation.

Let’s double-check C again — maybe it’s used.

C: $ 6(x+1) - 2 = -3x -14 $
→ $ 6x + 6 - 2 = 6x + ’t 4 $ → yes, 6x + 4
= –3x –14
→ 6x + 3x = –14 –4 → 9x = –18 → x = –2. Correct.

But –2 is not in the code, so C is unused.

What about the joke? “What rock group has four members that can’t sing or play instruments?”

Answer is likely: The Beatles? No, they do.

Wait — classic riddle:
“The Rolling Stones” — but they do play.

Another classic: “Led Zeppelin” — no.

Think differently: “rock group” could mean *geological rock*, and “four members that can’t sing or play instruments” → like statues? Mount Rushmore has 4 presidents — they’re carved in rock, can’t sing or play.

Ah! ✔ That’s it. Mount Rushmore is a *rock* group (group of rocks/statues), with four members (Washington, Jefferson, Roosevelt, Lincoln), and they can’t sing or play instruments.

So the revealed phrase is MOUNT RUSHMORE, and that answers the joke.

Thus, the final answer is the phrase formed: MOUNT RUSHMORE

But the code blanks are to be filled with letters, and the completed joke line should read:

M O U N T R U S H M O R E !

So the final answer is:
MOUNTRUSHMORE (or spaced).

Since the puzzle says “use the code to reveal the rest of the joke”, and the question is printed, the answer is the phrase.

Final Answer:
MOUNT RUSHMORE