Solve the equation x + sqrt(4) - 3x = -2.

Step-by-step solution

1. 1

   Evaluate the radical. $\sqrt{4}$ contains no variable, so it is just the number $2$ — note the principal square root is $+2$ only, not $\pm2$:

   $x + 2 - 3x = -2$

   Recognising this means the problem is a plain linear equation, not a radical equation, and no squaring or domain check is needed.

2. 2

   Combine the x terms.

   $x - 3x = -2x \quad\Longrightarrow\quad -2x + 2 = -2$

3. 3

   Subtract the constant.

   $-2x = -4$

4. 4

   Divide by the coefficient.

   $x = \frac{-4}{-2} = 2$

   Two negatives give a positive root — a sign slip here would produce $x = -2$.

5. 5

   Check in the original. $2 + \sqrt{4} - 3(2) = 2 + 2 - 6 = -2$, which is the right-hand side. Correct.