Solutions to linear equations displayed in a table format.

It looks like you've uploaded an image containing a table of equations and their corresponding solutions. The table is organized into three columns:

1. Equation (left column)
2. Intermediate step or simplified form (middle column)
3. Solution (value of x) (right column)

Let’s go through each row to verify the solutions and explain how they are solved.

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Row 1:

Equation: $ 4x = 16 $
Solution: $ x = 4 $
✔ Correct. Divide both sides by 4:
$ x = \frac{16}{4} = 4 $

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Row 2:

Equation: $ x + 10 = 24 $
Solution: $ x = 14 $
✔ Correct. Subtract 10 from both sides:
$ x = 24 - 10 = 14 $

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Row 3:

Equation: $ x - 14 = -6 $
Solution: $ x = 8 $
✔ Correct. Add 14 to both sides:
$ x = -6 + 14 = 8 $

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Row 4:

Equation: $ 12x = 144 $
Solution: $ x = 12 $
✔ Correct. Divide both sides by 12:
$ x = \frac{144}{12} = 12 $

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Row 5:

Equation: $ x + 9 = 6 $
Solution: $ x = -3 $
✔ Correct. Subtract 9 from both sides:
$ x = 6 - 9 = -3 $

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Row 6:

Equation: $ x - (-15) = 11 $ → $ x + 15 = 11 $
Solution: $ x = -4 $
✔ Correct. Subtract 15 from both sides:
$ x = 11 - 15 = -4 $

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Row 7:

Equation: $ x + 24 = 16 $
Solution: $ x = -8 $
✔ Correct. Subtract 24:
$ x = 16 - 24 = -8 $

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Row 8:

Equation: $ x - 7 = -21 $
Solution: $ x = -14 $
✔ Correct. Add 7:
$ x = -21 + 7 = -14 $

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Row 9:

Equation: $ -9x = -81 $
Solution: $ x = 9 $
✔ Correct. Divide both sides by -9:
$ x = \frac{-81}{-9} = 9 $

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Row 10:

Equation: $ x - 21 = -12 $
Solution: $ x = 9 $
✔ Correct. Add 21:
$ x = -12 + 21 = 9 $

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Row 11:

Equation: $ 4 + x = 36 $
Solution: $ x = 32 $
✔ Correct. Subtract 4:
$ x = 36 - 4 = 32 $

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Row 12:

Equation: $ -\frac{x}{8} = -4 $
Solution: $ x = 32 $
✔ Correct. Multiply both sides by -8:
$ x = (-4) \times (-8) = 32 $

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Summary:

All the solutions in the table are correct.

Each equation is linear in one variable ($x$), and the solution process involves basic algebraic operations:
- Adding/subtracting constants
- Multiplying/dividing by coefficients

The middle column sometimes shows intermediate steps, but not always. For example:
- In Row 10, $ x - 21 = -12 $ leads directly to $ x = 9 $
- In Row 12, $ -\frac{x}{8} = -4 $ implies multiplying both sides by -8

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Final Answer:

✔ All solutions provided in the table are correct.

If your task was to verify or solve these equations, then the table is accurate and complete. Let me know if you'd like a step-by-step breakdown for any specific equation!