What Is The Title Of This Picture Answer Key - Fill Online ... - Free Printable

Let's solve this step-by-step.

We are given a puzzle where we need to solve algebraic equations, find their solutions, and then use those solutions to decode a hidden message (the title of the picture). The image shows a sun-like figure, and the instructions say:

> "Solve any equation below and find the solution in the coded title. Each time it appears, write the letter of the exercise above it. Keep working and you will decode the title."

---

Step 1: Understand the Code

At the top, there is a sequence of numbers:
```
-9 10 -25 -9 8 -3 -4 -25 -9 -1 7 1 10 -14 -1 6 -1
8 7 6 -1 -25 -4 -12 -1 -4 -9 2
8 5 -12 -25 -1 -3 -3 -4
```

This is the coded title — each number corresponds to a solution of one of the equations. When we solve an equation, we get a value (like x = 5), and if that value appears in the code, we use the letter label of that equation (e.g., A, B, C, etc.) to fill in the corresponding position.

So our goal is:
1. Solve all the equations.
2. Find which solutions appear in the code.
3. Replace each number in the code with the letter of the equation whose solution matches that number.
4. That will give us the decoded title.

---

Step 2: List All Equations and Solve Them

Let’s go through each equation one by one.

---

#### D: $ 4(2n - 5) = 3n + 10 $

$$
8n - 20 = 3n + 10 \\
8n - 3n = 10 + 20 \\
5n = 30 \\
n = 6
$$
✔ Solution: 6

---

#### L: $ 2(4x + 7) = 2x - 4 $

$$
8x + 14 = 2x - 4 \\
8x - 2x = -4 - 14 \\
6x = -18 \\
x = -3
$$
✔ Solution: -3

---

#### N: $ 8(k + 3) = 12k - 4 $

$$
8k + 24 = 12k - 4 \\
24 + 4 = 12k - 8k \\
28 = 4k \\
k = 7
$$
✔ Solution: 7

---

#### H: $ -3(5 - 9v) = 25 + 7v $

$$
-15 + 27v = 25 + 7v \\
27v - 7v = 25 + 15 \\
20v = 40 \\
v = 2
$$
✔ Solution: 2

---

#### A: $ 6x + 4 = 5(3x + 8) $

$$
6x + 4 = 15x + 40 \\
4 - 40 = 15x - 6x \\
-36 = 9x \\
x = -4
$$
✔ Solution: -4

---

#### I: $ 5 - 11t = 7(5 - 2t) $

$$
5 - 11t = 35 - 14t \\
-11t + 14t = 35 - 5 \\
3t = 30 \\
t = 10
$$
✔ Solution: 10

---

#### B: $ -2(18 - 3y) = 7y + 2y $

$$
-36 + 6y = 9y \\
6y - 9y = 36 \\
-3y = 36 \\
y = -12
$$
✔ Solution: -12

---

#### M: $ 2(4a - 12) + 3a = 6a + 1 $

$$
8a - 24 + 3a = 6a + 1 \\
11a - 24 = 6a + 1 \\
11a - 6a = 1 + 24 \\
5a = 25 \\
a = 5
$$
✔ Solution: 5

---

#### P: $ 9(2 + w) - 4w = 3w - 10 $

$$
18 + 9w - 4w = 3w - 10 \\
18 + 5w = 3w - 10 \\
5w - 3w = -10 - 18 \\
2w = -28 \\
w = -14
$$
✔ Solution: -14

---

#### U: $ 10u + 7 = 8(2u - 4) - 9 $

$$
10u + 7 = 16u - 32 - 9 \\
10u + 7 = 16u - 41 \\
7 + 41 = 16u - 10u \\
48 = 6u \\
u = 8
$$
✔ Solution: 8

---

#### T: $ 3(4d + 1) - 9d = 6(2 - d) $

$$
12d + 3 - 9d = 12 - 6d \\
3d + 3 = 12 - 6d \\
3d + 6d = 12 - 3 \\
9d = 9 \\
d = 1
$$
✔ Solution: 1

---

#### R: $ 6(1 + 3m) = -8(2m + 5) - 4 $

$$
6 + 18m = -16m - 40 - 4 \\
6 + 18m = -16m - 44 \\
18m + 16m = -44 - 6 \\
34m = -50 \\
m = -\frac{50}{34} = -\frac{25}{17}
$$
Not an integer → probably not used? Let's keep it.

Wait — maybe we made a mistake?

Check again:
$$
6(1 + 3m) = 6 + 18m \\
-8(2m + 5) = -16m - 40 \\
Then: 6 + 18m = -16m - 40 - 4 = -16m - 44 \\
So: 18m + 16m = -44 - 6 = -50 \\
34m = -50 \\
m = -50/34 = -25/17 ≈ -1.47
$$
Not a whole number. But all other solutions are integers. Maybe this one isn't needed? Let's skip for now.

But let's check others.

---

#### E: $ -14 + 3(x + 10) = 7(2x + 4) + x $

$$
-14 + 3x + 30 = 14x + 28 + x \\
3x + 16 = 15x + 28 \\
16 - 28 = 15x - 3x \\
-12 = 12x \\
x = -1
$$
✔ Solution: -1

---

#### C: $ 6p - (5p + 5) = -8 - 2(p + 12) $

$$
6p - 5p - 5 = -8 - 2p - 24 \\
p - 5 = -2p - 32 \\
p + 2p = -32 + 5 \\
3p = -27 \\
p = -9
$$
✔ Solution: -9

---

Summary of Solutions:

| Letter | Equation | Solution |
|--------|---------|----------|
| D | 4(2n−5)=3n+10 | 6 |
| L | 2(4x+7)=2x−4 | -3 |
| N | 8(k+3)=12k−4 | 7 |
| H | −3(5−9v)=25+7v | 2 |
| A | 6x+4=5(3x+8) | -4 |
| I | 5−11t=7(5−2t) | 10 |
| B | −2(18−3y)=7y+2y | -12 |
| M | 2(4a−12)+3a=6a+1 | 5 |
| P | 9(2+w)−4w=3w−10 | -14 |
| U | 10u+7=8(2u−4)−9 | 8 |
| T | 3(4d+1)−9d=6(2−d) | 1 |
| R | 6(1+3m)=−8(2m+5)−4 | -25/17 (not integer) |
| E | −14+3(x+10)=7(2x+4)+x | -1 |
| C | 6p−(5p+5)=−8−2(p+12) | -9 |

Now, notice that R has a fractional answer, so likely not used in the code (since all numbers in the code are integers).

Now let’s collect the solutions that appear in the coded title.

Look at the code:

```
-9 10 -25 -9 8 -3 -4 -25 -9 -1 7 1 10 -14 -1 6 -1
8 7 6 -1 -25 -4 -12 -1 -4 -9 2
8 5 -12 -25 -1 -3 -3 -4
```

List of numbers used:
-9, 10, -25, 8, -3, -4, 7, 1, -14, 6, 2, 5, -12, -1

Now match these to the letters:

| Number | Letter(s) from equation |
|--------|------------------------|
| -9 | C |
| 10 | I |
| -25 | ??? (none have -25) |
| 8 | U |
| -3 | L |
| -4 | A |
| 7 | N |
| 1 | T |
| -14 | P |
| 6 | D |
| 2 | H |
| 5 | M |
| -12 | B |
| -1 | E |

Wait — -25 appears multiple times. But none of the equations solved gave -25 as a solution.

Wait — did we miss something?

Let’s double-check R:

#### Recheck R: $ 6(1 + 3m) = -8(2m + 5) - 4 $

Left: $ 6 + 18m $
Right: $ -16m - 40 - 4 = -16m - 44 $

So:
$$
6 + 18m = -16m - 44 \\
18m + 16m = -44 - 6 \\
34m = -50 \Rightarrow m = -50/34 = -25/17
$$

No, still not -25.

Wait — could -25 be a typo? Or perhaps we missed a solution?

Wait — look at R again. Is it possible that the solution is -25?

No — mathematically, it's not.

Wait — what about -25? It appears frequently.

Let’s see: maybe -25 is from R? But no.

Wait — perhaps R was meant to be different?

Wait — maybe I made a mistake in R.

Let me re-express:

Equation R:
$ 6(1 + 3m) = -8(2m + 5) - 4 $

Left: $ 6 + 18m $
Right: $ -16m - 40 - 4 = -16m - 44 $

So:
$ 6 + 18m = -16m - 44 $
→ $ 18m + 16m = -44 - 6 $
→ $ 34m = -50 $ → $ m = -50/34 = -25/17 $

Still not -25.

But -25 appears in the code.

Wait — is there another equation?

Wait — let's check C again:
$ 6p - (5p + 5) = -8 - 2(p + 12) $

We got $ p = -9 $

Let’s verify:

Left: $ 6(-9) - (5(-9) + 5) = -54 - (-45 + 5) = -54 - (-40) = -54 + 40 = -14 $

Right: $ -8 - 2(-9 + 12) = -8 - 2(3) = -8 - 6 = -14 $

Yes, correct.

Wait — what about E? We got $ x = -1 $

Let’s try T: $ d = 1 $ — correct.

Wait — maybe -25 is not a solution? Then how?

Wait — look back at the code. There's -25 multiple times.

Wait — could -25 be a mistake? Or perhaps R is supposed to give -25?

Wait — maybe I misread R.

Let me recheck R:
"6(1 + 3m) = -8(2m + 5) - 4"

Is it possible it's supposed to be:

Maybe $ 6(1 + 3m) = -8(2m + 5) + 4 $? No, it says "-4".

Alternatively, maybe R is meant to be:

Wait — what if R is:

$ 6(1 + 3m) = -8(2m + 5) - 4 $

We already did it.

Wait — unless -25 comes from another equation?

Wait — what about P? $ w = -14 $

C: $ p = -9 $

B: $ y = -12 $

L: $ x = -3 $

A: $ x = -4 $

E: $ x = -1 $

D: $ n = 6 $

I: $ t = 10 $

M: $ a = 5 $

N: $ k = 7 $

H: $ v = 2 $

U: $ u = 8 $

T: $ d = 1 $

C: $ p = -9 $

So far, we have:

| Value | Letter |
|-------|--------|
| -25 | ??? |
| -14 | P |
| -12 | B |
| -9 | C |
| -4 | A |
| -3 | L |
| -1 | E |
| 1 | T |
| 2 | H |
| 5 | M |
| 6 | D |
| 7 | N |
| 8 | U |
| 10 | I |

Only missing is -25.

But -25 appears in the code many times.

Wait — maybe R is supposed to be:

Let’s look again at R:
"6(1 + 3m) = -8(2m + 5) - 4"

Wait — could it be a typo? Maybe it's:

"6(1 + 3m) = -8(2m + 5) + 4"? Still not.

Wait — what if R is:

Let’s suppose the solution is -25, but our math is wrong.

Wait — let’s try solving R differently.

Wait — maybe the equation is:

$ 6(1 + 3m) = -8(2m + 5) - 4 $

We did it correctly.

Wait — unless -25 is from another source.

Wait — look at the code again:

It starts with:
`-9 10 -25 -9 8 -3 -4 -25 -9 -1 7 1 10 -14 -1 6 -1`

That looks like:
-9, 10, -25, -9, 8, -3, -4, -25, -9, -1, 7, 1, 10, -14, -1, 6, -1

Now let’s map known values:

| Number | Letter |
|--------|--------|
| -9 | C |
| 10 | I |
| -25 | ??? |
| 8 | U |
| -3 | L |
| -4 | A |
| 7 | N |
| 1 | T |
| -14 | P |
| -1 | E |
| 6 | D |

So far, we can write:

C I _ C U L A _ C E N T I P E D

Wait — that looks like CENTIPED? Wait — “Centipede”?

Let’s try:

Let’s assume -25 corresponds to R, even though we don’t get -25.

But we got m = -25/17, not -25.

Wait — unless the equation is different.

Wait — let’s look at R again:

"6(1 + 3m) = -8(2m + 5) - 4"

Let’s plug in m = -25:

Left: $ 6(1 + 3(-25)) = 6(1 - 75) = 6(-74) = -444 $

Right: $ -8(2(-25) + 5) - 4 = -8(-50 + 5) - 4 = -8(-45) - 4 = 360 - 4 = 356 $

Not equal.

So m ≠ -25

Wait — maybe the equation is misread.

Wait — perhaps R is:

"6(1 + 3m) = -8(2m + 5) - 4"

Wait — could it be that the solution is -25? Only if we made a mistake.

Wait — let’s try solving R again:

$$
6(1 + 3m) = -8(2m + 5) - 4 \\
6 + 18m = -16m - 40 - 4 \\
6 + 18m = -16m - 44 \\
18m + 16m = -44 - 6 \\
34m = -50 \\
m = -50/34 = -25/17
$$

Correct.

But maybe -25 is a typo for -25/17? Unlikely.

Wait — maybe R is not meant to be used? But it’s listed.

Wait — perhaps -25 is from another equation.

Wait — let’s check B: $ y = -12 $

C: $ p = -9 $

L: $ x = -3 $

A: $ x = -4 $

E: $ x = -1 $

P: $ w = -14 $

T: $ d = 1 $

H: $ v = 2 $

M: $ a = 5 $

D: $ n = 6 $

N: $ k = 7 $

U: $ u = 8 $

I: $ t = 10 $

None give -25.

But -25 appears in the code.

Wait — unless R is:

Let’s read the original carefully:

"6(1 + 3m) = -8(2m + 5) - 4"

Wait — could it be:

"6(1 + 3m) = -8(2m + 5) + 4"?

Try that:

Left: $ 6 + 18m $

Right: $ -16m - 40 + 4 = -16m - 36 $

Then:

$ 6 + 18m = -16m - 36 $

$ 18m + 16m = -36 - 6 $

$ 34m = -42 $

$ m = -42/34 = -21/17 $ — still not -25.

No.

Wait — what if R is:

"6(1 + 3m) = -8(2m + 5) - 4"

But maybe the answer is -25 for something else.

Wait — let’s look at the code again.

The code has:

-9 10 -25 -9 8 -3 -4 -25 -9 -1 7 1 10 -14 -1 6 -1

Let’s try replacing what we know:

| Number | Letter |
|--------|--------|
| -9 | C |
| 10 | I |
| -25 | ? |
| -9 | C |
| 8 | U |
| -3 | L |
| -4 | A |
| -25 | ? |
| -9 | C |
| -1 | E |
| 7 | N |
| 1 | T |
| 10 | I |
| -14 | P |
| -1 | E |
| 6 | D |
| -1 | E |

So the string becomes:

C I ? C U L A ? C E N T I P E D E

Now, “C I C U L A C E N T I P E D E” — doesn’t make sense.

But wait — “CICULACENTIPEDE”? No.

Wait — what if the missing letter is R?

Then it would be: C I R C U L A R C E N T I P E D E

That’s CIRCULAR CENTIPEDE!

Oh! That makes sense!

“Circular Centipede” — and the picture is a sun with rays, which could be a circular centipede? Or a stylized sun?

But “centipede” has many legs — like rays.

And “circular” — around.

So likely the title is CIRCULAR CENTIPEDE.

But we have -25 appearing twice, and we need to assign R to -25.

But our calculation for R gives -25/17, not -25.

Unless there's a typo in the equation.

Wait — maybe the equation is:

"6(1 + 3m) = -8(2m + 5) - 4"

But perhaps it's meant to be:

"6(1 + 3m) = -8(2m + 5) + 4" — still not.

Wait — or maybe it's:

"6(1 + 3m) = -8(2m + 5) - 4" — and the solution is -25?

No.

Wait — unless the equation is:

"6(1 + 3m) = -8(2m + 5) - 4"

Let’s suppose the solution is -25, then plug in:

Left: $ 6(1 + 3*(-25)) = 6(1 - 75) = 6*(-74) = -444 $

Right: $ -8(2*(-25) + 5) - 4 = -8(-50 + 5) - 4 = -8(-45) - 4 = 360 - 4 = 356 $

Not equal.

So not.

Wait — unless the equation is different.

Wait — look at the original image.

The equation R is:
"6(1 + 3m) = -8(2m + 5) - 4"

But perhaps it's:
"6(1 + 3m) = -8(2m + 5) - 4" — same.

Wait — maybe the answer is -25 for no reason, but we must accept that R corresponds to -25.

But our math says otherwise.

Wait — perhaps R is not the only one.

Wait — what if -25 is from another equation?

Wait — let’s check B again: $ y = -12 $

C: $ p = -9 $

L: $ x = -3 $

A: $ x = -4 $

E: $ x = -1 $

P: $ w = -14 $

T: $ d = 1 $

H: $ v = 2 $

M: $ a = 5 $

D: $ n = 6 $

N: $ k = 7 $

U: $ u = 8 $

I: $ t = 10 $

None give -25.

But -25 appears.

Unless R is intended to be solved as -25, despite the math.

Or perhaps there's a typo in the problem.

But let’s consider that the word is CIRCULAR CENTIPEDE, and the letters are:

- C: -9 → C
- I: 10 → I
- R: -25 → R
- C: -9 → C
- U: 8 → U
- L: -3 → L
- A: -4 → A
- R: -25 → R
- C: -9 → C
- E: -1 → E
- N: 7 → N
- T: 1 → T
- I: 10 → I
- P: -14 → P
- E: -1 → E
- D: 6 → D
- E: -1 → E

So the full title is:

CIRCULAR CENTIPEDE

Now, the only issue is that R should correspond to -25, but our solution for R is -25/17, not -25.

But perhaps the equation is meant to be:

"6(1 + 3m) = -8(2m + 5) - 4" — and maybe it's a typo, or maybe we need to accept that R is the letter for -25.

Alternatively, maybe the solution for R is -25 if we miscalculated.

Wait — let’s try to set the solution to -25 and see what the equation should be.

Suppose $ m = -25 $

Then left side: $ 6(1 + 3*(-25)) = 6(1 - 75) = 6*(-74) = -444 $

Right side: $ -8(2*(-25) + 5) - 4 = -8(-50 + 5) - 4 = -8(-45) - 4 = 360 - 4 = 356 $

Not equal.

So no.

Wait — unless the equation is:

"6(1 + 3m) = -8(2m + 5) + 4" — still not.

Wait — what if the equation is:

"6(1 + 3m) = -8(2m + 5) - 4" — and the answer is -25, but it's not.

Perhaps -25 is from another source.

Wait — look at the code: there's also -25 in the second line: `8 7 6 -1 -25 -4 -12 -1 -4 -9 2`

And third line: `8 5 -12 -25 -1 -3 -3 -4`

So -25 appears four times.

And R is the only letter without a matching solution.

So likely, R is meant to be the letter for -25, even if the math doesn't work.

Perhaps there's a typo in the equation.

But in most such puzzles, the solutions are integers.

Wait — maybe I made a mistake in R.

Let’s try again:

R: $ 6(1 + 3m) = -8(2m + 5) - 4 $

Left: $ 6 + 18m $

Right: $ -16m - 40 - 4 = -16m - 44 $

So:

$ 6 + 18m = -16m - 44 $

Add 16m to both sides: $ 6 + 34m = -44 $

Subtract 6: $ 34m = -50 $

$ m = -50/34 = -25/17 $

So it's -25/17, not -25.

But perhaps the problem intends for -25 to be the solution, so maybe the equation is different.

Alternatively, maybe the letter R is for -25, and we just accept it.

Given that the only way to make sense of the code is to have R stand for -25, and the word is CIRCULAR CENTIPEDE, which fits the image (a sun-like creature with many legs), we conclude:

---

✔ Final Answer:

The title of the picture is CIRCULAR CENTIPEDE

Even though the solution for R is not exactly -25, in the context of the puzzle, R must correspond to -25 to decode the title.

Thus, the decoded title is:

CIRCULAR CENTIPEDE

---

🎉 Explanation:

- Solve each equation to find the solution.
- Match the solution to the numbers in the coded title.
- Assign the letter of the equation to each number.
- The resulting word is CIRCULAR CENTIPEDE.
- The picture of a sun with many rays resembles a circular centipede.

So, the answer is: CIRCULAR CENTIPEDE