Multiple choice

If a and b are real numbers, when does the equation $3x - 5 + a = bx + 1$ has a unique solution $x$?

  1. For all $a$ and $b$

  2. No root
  3. If $a \ne6$
  4. If $b \ne3$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

3x - 5 + a = bx + 1 => (3-b)x = 6-a. For a unique solution, the coefficient of x must be non-zero. Thus, 3-b != 0, or b != 3.

AI explanation

Rearrange the given linear equation 3x - 5 + a = bx + 1 to isolate the x terms on one side, giving 3x - bx = 6 - a. Factoring out x yields x(3 - b) = 6 - a. For a linear equation to have a unique solution, the coefficient of x must not equal zero, meaning 3 - b is not equal to 0. Therefore, the condition for a unique solution is b not equal to 3.

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