Algebra

Common Misconceptions (Algebra)

Algebra Missteps

         

What are the solution(s) to the equation x+4=x2?\sqrt{x+ 4} = x -2?

(Partial solution)
The equation can be rewritten as follows: x+4=x2x+4=(x2)2x+4=x24x+40=x25x0=x(x5).\begin{aligned} \sqrt{x+ 4} &= x -2\\ x+ 4 &= (x -2)^2\\ x+ 4 &= x^2 - 4x + 4\\ 0 &= x^2 - 5x\\ 0 &= x(x - 5). \end{aligned}

Where is the error in the solution to this problem?

Find the solution set of 20x>520 - x > 5.

Line 1. 20x>5\,\,\,\,\,20 - x > 5

Line 2. x>15\,\,\,\,\,-x > -15

Line 3. x>15\,\,\,\,\,x >15

Where is the error in the solution to this problem?

Find the solution set of 3x<83 - x < 8.

Step 1. 3x<8\,\,\,\,\,3 - x < 8

Step 2. x<5\,\,\,\,\,-x < 5

Step 3. x<5\,\,\,\,\,x < -5

Is the following solution valid?

  1. x5=3\,\,\,\,\,\sqrt{x - 5} = -3

  2. x5=9\,\,\,\,\,x - 5 = 9

  3. x=14\,\,\,\,\,x = 14

Consider the following work done to solve the equation x+1=1.\sqrt{x + 1} = 1.

  1. x+1=1\,\,\,\,\,\sqrt{x} + \sqrt{1} = 1

  2. x+1=1\,\,\,\,\,\sqrt{x} + 1 = 1

  3. x=0\,\,\,\,\,\sqrt{x} = 0

  4. x=0\,\,\,\,\,x = 0

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