We are given the equation:

\[
35x - 21 - 10 = 6x - 10 - 15 + 21x
\]

Let's solve it step by step:

### Step 1: Simplify both sides.
On the left-hand side:
\[
35x - 21 - 10 = 35x - 31
\]

On the right-hand side, combine like terms:
\[
6x - 10 - 15 + 21x = 6x + 21x - 10 - 15 = 27x - 25
\]

Now the equation looks like:
\[
35x - 31 = 27x - 25
\]

### Step 2: Move all terms involving \(x\) to one side.
Subtract \(27x\) from both sides:
\[
35x - 27x - 31 = -25
\]
\[
8x - 31 = -25
\]

### Step 3: Move constant terms to the other side.
Add \(31\) to both sides:
\[
8x = -25 + 31
\]
\[
8x = 6
\]

### Step 4: Solve for \(x\).
Divide both sides by 8:
\[
x = \frac{6}{8} = \frac{3}{4}
\]

So, the solution is:
\[
x = \frac{3}{4}
\]

Would you like more details on any part of this process or have any other questions?

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Here are 5 related questions to practice:

1. Solve \( 5x - 4 = 3x + 10 \).
2. Solve \( 12x - 9 = 4x + 15 \).
3. Solve \( 2x - 7 = 6x + 1 - 5x \).
4. Solve \( 8x + 3 = 6x - 9 + 4x \).
5. Solve \( 10x - 5 - 3x = 7x - 20 \).

**Tip:** Always combine like terms first to simplify equations, making solving easier!

Learn how to solve the linear equation 35x - 21 - 10 = 6x - 10 - 15 + 21x with a detailed step-by-step solution. This problem covers key algebraic concepts, including combining like terms and solving for x. Suitable for students in Grades 8-10.

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