square root of 10 space minus space 3 x end root space equals space x﻿

The equation given is:

\[
\sqrt{10} - 3x = x
\]

Let's solve for \( x \):

### Step 1: Move all terms involving \( x \) to one side of the equation.

\[
\sqrt{10} = x + 3x
\]

\[
\sqrt{10} = 4x
\]

### Step 2: Solve for \( x \).

\[
x = \frac{\sqrt{10}}{4}
\]

### Step 3: Approximate the square root of 10.

\[
\sqrt{10} \approx 3.162
\]

Thus,

\[
x = \frac{3.162}{4} \approx 0.7905
\]

The solution is approximately:

\[
x \approx 0.7905
\]

Would you like further details or have any questions?

Here are five related questions for further practice:
1. Solve \(\sqrt{20} - 2x = x\).
2. What is the square root of 15 minus \(4x = x\)?
3. Solve \(2\sqrt{6} - 3x = x\).
4. If \(\sqrt{8} - x = 2x\), what is the value of \(x\)?
5. Solve for \(x\): \(\sqrt{12} - 5x = 2x\).

**Tip:** When dealing with square roots, always isolate the terms involving the square root before solving for \(x\).

Explore how to solve the equation \(\sqrt{10} - 3x = x\) step-by-step. This problem involves key algebraic concepts such as square roots and linear equations. Suitable for students in Grades 8-10.

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