Math worksheet for solving two-step equations with a color-by-number activity.

Let's solve each two-step equation step by step and then determine the correct color based on the solution. The goal is to solve for $ x $ in each equation, and then use the answer to find the corresponding color code.

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Problem 1:

Equation: $-7x + 16 = 58$
Solve:

$$
-7x + 16 = 58 \\
-7x = 58 - 16 \\
-7x = 42 \\
x = \frac{42}{-7} \\
x = -6
$$

✔ Answer: $ x = -6 $ → Color: Red

---

Problem 2:

Equation: $-2x + 15 = -9$
Solve:

$$
-2x + 15 = -9 \\
-2x = -9 - 15 \\
-2x = -24 \\
x = \frac{-24}{-2} \\
x = 12
$$

✔ Answer: $ x = 12 $ → Color: Green

---

Problem 3:

Equation: $5x - 4 = 36$
Solve:

$$
5x - 4 = 36 \\
5x = 36 + 4 \\
5x = 40 \\
x = \frac{40}{5} \\
x = 8
$$

✔ Answer: $ x = 8 $ → Color: Purple

---

Problem 4:

Equation: $25 - 3x = 88$
Solve:

$$
25 - 3x = 88 \\
-3x = 88 - 25 \\
-3x = 63 \\
x = \frac{63}{-3} \\
x = -21
$$

✔ Answer: $ x = -21 $ → Color: Orange

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Problem 5:

Equation: $-11 = 7 - x$
Solve:

$$
-11 = 7 - x \\
-11 - 7 = -x \\
-18 = -x \\
x = 18
$$

✔ Answer: $ x = 18 $ → Color: Pink

---

Problem 6:

Equation: $65 + 15x = 35$
Solve:

$$
65 + 15x = 35 \\
15x = 35 - 65 \\
15x = -30 \\
x = \frac{-30}{15} \\
x = -2
$$

✔ Answer: $ x = -2 $ → Color: Yellow

---

Problem 7:

Equation: $\frac{1}{2}x - 18 = 2$
Solve:

$$
\frac{1}{2}x - 18 = 2 \\
\frac{1}{2}x = 2 + 18 \\
\frac{1}{2}x = 20 \\
x = 20 \times 2 \\
x = 40
$$

✔ Answer: $ x = 40 $ → Color: Blue

---

Problem 8:

Equation: $\frac{2}{3}x - 10 = -12$
Solve:

$$
\frac{2}{3}x - 10 = -12 \\
\frac{2}{3}x = -12 + 10 \\
\frac{2}{3}x = -2 \\
x = -2 \times \frac{3}{2} \\
x = -3
$$

✔ Answer: $ x = -3 $ → Color: Orange

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Problem 9:

Equation: $6 - \frac{1}{3}x = -1$
Solve:

$$
6 - \frac{1}{3}x = -1 \\
-\frac{1}{3}x = -1 - 6 \\
-\frac{1}{3}x = -7 \\
x = (-7) \times (-3) \\
x = 21
$$

✔ Answer: $ x = 21 $ → Color: Yellow

---

Problem 10:

Equation: $4 - 9x = -14$
Solve:

$$
4 - 9x = -14 \\
-9x = -14 - 4 \\
-9x = -18 \\
x = \frac{-18}{-9} \\
x = 2
$$

✔ Answer: $ x = 2 $ → Color: Blue

---

Problem 11:

Equation: $11 - x = 29$
Solve:

$$
11 - x = 29 \\
-x = 29 - 11 \\
-x = 18 \\
x = -18
$$

✔ Answer: $ x = -18 $ → Color: Orange

---

Problem 12:

Equation: $-9 - 11x = 68$
Solve:

$$
-9 - 11x = 68 \\
-11x = 68 + 9 \\
-11x = 77 \\
x = \frac{77}{-11} \\
x = -7
$$

✔ Answer: $ x = -7 $ → Color: Yellow

---

Problem 13:

Equation: $45 + \frac{5}{6}x = 50$
Solve:

$$
45 + \frac{5}{6}x = 50 \\
\frac{5}{6}x = 50 - 45 \\
\frac{5}{6}x = 5 \\
x = 5 \times \frac{6}{5} \\
x = 6
$$

✔ Answer: $ x = 6 $ → Color: Orange

---

Problem 14:

Equation: $-5x + 17 = -33$
Solve:

$$
-5x + 17 = -33 \\
-5x = -33 - 17 \\
-5x = -50 \\
x = \frac{-50}{-5} \\
x = 10
$$

✔ Answer: $ x = 10 $ → Color: Red

---

Problem 15:

Equation: $95 = -4 + 33x$
Solve:

$$
95 = -4 + 33x \\
95 + 4 = 33x \\
99 = 33x \\
x = \frac{99}{33} \\
x = 3
$$

✔ Answer: $ x = 3 $ → Color: Purple

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✔ Final Answer Summary:

| Problem | Equation | Solution | Color |
|--------|---------|----------|-------|
| 1 | $-7x+16=58$ | $x = -6$ | Red |
| 2 | $-2x+15=-9$ | $x = 12$ | Green |
| 3 | $5x-4=36$ | $x = 8$ | Purple |
| 4 | $25-3x=88$ | $x = -21$ | Orange |
| 5 | $-11=7-x$ | $x = 18$ | Pink |
| 6 | $65+15x=35$ | $x = -2$ | Yellow |
| 7 | $\frac{1}{2}x - 18 = 2$ | $x = 40$ | Blue |
| 8 | $\frac{2}{3}x - 10 = -12$ | $x = -3$ | Orange |
| 9 | $6 - \frac{1}{3}x = -1$ | $x = 21$ | Yellow |
| 10 | $4 - 9x = -14$ | $x = 2$ | Blue |
| 11 | $11 - x = 29$ | $x = -18$ | Orange |
| 12 | $-9 - 11x = 68$ | $x = -7$ | Yellow |
| 13 | $45 + \frac{5}{6}x = 50$ | $x = 6$ | Orange |
| 14 | $-5x + 17 = -33$ | $x = 10$ | Red |
| 15 | $95 = -4 + 33x$ | $x = 3$ | Purple |

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🎨 Coloring Instructions:

Now, on the coloring page (not shown), you will:
- Find each solution ($x = -6$, $x = 12$, etc.) and locate it.
- Color that region with the corresponding color listed above.
- Ensure symmetry as instructed.

For example:
- All regions with $x = -6$ → Red
- All regions with $x = 12$ → Green
- And so on.

This activity reinforces solving two-step equations while engaging creativity through coloring.

Let me know if you'd like a printable version or help visualizing the final colored image!