Question

HELP PLEASE ITS DUE IN 10 MIN Use algebraic strategies to solve for x.

Check your solutions algebraically and identify any extraneous solutions. Write it step by step.

Answer 1

x = 4, x ≠ -1

Explanation:

√3x + 4 = x

(√3x + 4)² = x² (Square both sides to get rid of the radical.)

3x + 4 = x²

0 = x² - 3x - 4 (Set everything to 0 by moving everything to one side.)

0 = (x - 4)(x + 1) (Factor.)

x = 4 x = -1

Now we need to check for extraneous solutions:

√3(4) + 4 = 4

√12 + 4 = 4

√16 = 4

4 = 4

√3(-1) + 4 = -1

√-3 +4 = -1

√1 = -1

1 ≠ -1

-1 is an extraneous solution.