One Step Equations with Integers Triangle Puzzle - Free Printable

Let’s solve each equation one by one. We’re looking for the value of x in each case. These are all one-step equations with integers, so we’ll use inverse operations to isolate x.

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We’ll go piece by piece and solve each equation:

1. x + 17 = -31
Subtract 17 from both sides:
x = -31 - 17 = -48

2. 12 + x = -6
Subtract 12 from both sides:
x = -6 - 12 = -18

3. -5x = 150
Divide both sides by -5:
x = 150 ÷ (-5) = -30

4. x - 9 = -6
Add 9 to both sides:
x = -6 + 9 = 3

5. -8 + x = -17 → same as x - 8 = -17
Add 8 to both sides:
x = -17 + 8 = -9

6. -8x = 56
Divide both sides by -8:
x = 56 ÷ (-8) = -7

7. x = -110 → already solved! So x = -110

8. x/11 = -10
Multiply both sides by 11:
x = -10 × 11 = -110

9. x = -12 → already solved! So x = -12

10. x = -8 → already solved! So x = -8

11. x = 48 → already solved! So x = 48

12. x = -17 → already solved! So x = -17

13. x + 17 = 6 → wait, no — it says “x + 17 = 6”? Let me check again.

Wait — actually, looking at the puzzle pieces, some are written upside down or rotated. But since we’re solving mathematically, let’s just solve what’s written clearly.

Actually, let’s list all unique equations from the image (ignoring duplicates and focusing on distinct ones):

From top row:
- B: x + 17 = -31 → x = -48
- P: 12 + x = -6 → x = -18

Left side:
- N: -5x = 150 → x = -30
- J: x - 9 = -6 → x = 3
- Also: -8 + x = -17 → x = -9
- And: -8x = 56 → x = -7
- And: x = -110 (appears twice? Once as solution, once as equation?)

Middle:
- O: x = -110 (solution)
- A: x/11 = -10 → x = -110
- R: x = -12
- Also: x = -8
- Also: x = 48

Right side:
- I: x/7 = -15 → x = -105
- C: x + 17 = 6? Wait — looks like “x + 17 = 6” but that would be x = -11 — but maybe it’s “x + 17 = -6”? No, let’s read carefully.

Actually, in the right triangle labeled “C”, it says:
“x + 17 = 6” → then x = 6 - 17 = -11

But below it says “x = -9” — that must be a different piece.

Wait — perhaps better to group by lettered triangles and solve each equation associated with them.

Let me assign each lettered triangle its equation and solve:

Triangle B: x + 17 = -31 → x = -48
Triangle P: 12 + x = -6 → x = -18
Triangle N: -5x = 150 → x = -30
Triangle J: x - 9 = -6 → x = 3
Triangle O: x = -110 (given)
Triangle A: x/11 = -10 → x = -110
Triangle R: x = -12 (given)
Triangle I: x/7 = -15 → x = -105
Triangle C: x + 17 = 6 → x = -11
Triangle H: -15 + x = -8 → x = 7
Triangle F: -3x = -21 → x = 7
Triangle M: 7x = -35 → x = -5
Triangle Q: x/-30 = -10 → x = 300
Triangle G: x/-7 = -15 → x = 105? Wait — let's see.

Wait — Triangle G says: “x / -7 = -15” → multiply both sides by -7: x = (-15)*(-7) = 105

But below it says “x = 13” — that must be another piece.

Triangle E: 11x = 143 → x = 13
Triangle D: x - 36 = -10 → x = 26
Triangle L: 15 - x = 21 → subtract 15: -x = 6 → x = -6
Triangle K: x/-3 = -16 → multiply both sides by -3: x = 48
Triangle Y: x - 7 = -19 → x = -12
Triangle V: ? Not sure — maybe duplicate.

Also, there’s a piece that says “x = 26” — matches D
“x = 7” — matches H and F
“x = -5” — matches M
“x = 300” — matches Q
“x = 13” — matches E
“x = -6” — matches L
“x = 48” — matches K and also appears elsewhere
“x = -12” — matches R and Y
“x = -18” — matches P
“x = -48” — matches B
“x = -30” — matches N
“x = 3” — matches J
“x = -9” — where does this come from? From “-8 + x = -17” → x = -9
“x = -7” — from “-8x = 56” → x = -7
“x = -110” — from A and O
“x = -105” — from I
“x = -11” — from C? But C says x + 17 = 6 → x = -11
“x = 105” — from G? If G is x/-7 = -15 → x = 105

But wait — in the bottom right, triangle E says “11x = 143” → x = 13
And next to it, “x = 300” — which comes from Q: x/-30 = -10 → x = 300

Now, let’s verify a few key ones to make sure:

Check Triangle Q: x / (-30) = -10 → x = (-10) * (-30) = 300 ✔
Check Triangle I: x / 7 = -15 → x = -105 ✔
Check Triangle G: x / (-7) = -15 → x = 105 ✔
Check Triangle L: 15 - x = 21 → -x = 6 → x = -6 ✔
Check Triangle D: x - 36 = -10 → x = 26 ✔
Check Triangle M: 7x = -35 → x = -5 ✔
Check Triangle F: -3x = -21 → x = 7 ✔
Check Triangle H: -15 + x = -8 → x = 7 ✔
Check Triangle C: x + 17 = 6 → x = -11 ✔
Check Triangle Y: x - 7 = -19 → x = -12 ✔
Check Triangle K: x / (-3) = -16 → x = 48 ✔
Check Triangle N: -5x = 150 → x = -30 ✔
Check Triangle J: x - 9 = -6 → x = 3 ✔
Check Triangle B: x + 17 = -31 → x = -48 ✔
Check Triangle P: 12 + x = -6 → x = -18 ✔
Check Triangle A: x/11 = -10 → x = -110 ✔
Check Triangle R: x = -12 (given) ✔
Check Triangle O: x = -110 (given) ✔
Check Triangle E: 11x = 143 → x = 13 ✔

Now, notice that some solutions appear multiple times — that’s how the puzzle matches up.

For example:
- x = -110 appears for both A and O
- x = -12 appears for R and Y
- x = 7 appears for H and F
- x = 48 appears for K and also as a standalone solution

So the matching is based on pairing equations with their correct solutions.

Since the task is to match equations and solutions to complete the puzzle, and we’ve solved all equations, the final answer isn’t a single number — it’s the set of matched pairs.

But the user asked to “solve the problem accurately” — and since it’s a puzzle, perhaps they want the value of x for each labeled triangle? Or maybe the completed puzzle configuration?

Looking back at the directions: “Match equations and solutions to complete the puzzle.”

But since we can’t physically cut and paste here, and the user likely wants the solutions verified, I think the best approach is to list each lettered triangle with its correct solution.

Let me compile a clean list:

- B: x + 17 = -31 → x = -48
- P: 12 + x = -6 → x = -18
- N: -5x = 150 → x = -30
- J: x - 9 = -6 → x = 3
- O: x = -110 → x = -110
- A: x/11 = -10 → x = -110
- R: x = -12 → x = -12
- I: x/7 = -15 → x = -105
- C: x + 17 = 6 → x = -11
- H: -15 + x = -8 → x = 7
- F: -3x = -21 → x = 7
- M: 7x = -35 → x = -5
- Q: x/-30 = -10 → x = 300
- G: x/-7 = -15 → x = 105
- E: 11x = 143 → x = 13
- D: x - 36 = -10 → x = 26
- L: 15 - x = 21 → x = -6
- K: x/-3 = -16 → x = 48
- Y: x - 7 = -19 → x = -12

Note: Some letters might be missing or duplicated due to rotation, but these are all the distinct equations visible.

Now, to confirm, let’s pick one that might be tricky: Triangle G.

It says: “x / -7 = -15”

Multiply both sides by -7:
x = (-15) * (-7) = 105 → correct.

Another: Triangle Q: “x / -30 = -10”
x = (-10) * (-30) = 300 → correct.

Triangle L: “15 - x = 21”
Subtract 15: -x = 6 → x = -6 → correct.

All checks out.

Final Answer: The solutions for each labeled triangle are as follows:

B: -48
P: -18
N: -30
J: 3
O: -110
A: -110
R: -12
I: -105
C: -11
H: 7
F: 7
M: -5
Q: 300
G: 105
E: 13
D: 26
L: -6
K: 48
Y: -12

(Note: Since the puzzle requires matching, these values should be paired with their corresponding equation pieces to assemble the hexagon correctly.)