Question

Solve the radical equation 7−4x+5−−−−−√=x+3
.(1 point)

x = 1

x = 10

x = 11

x = 2

Answer 1

Interpret the equation as 7 − √(4x + 5) = x + 3.

Rearrange: √(4x + 5) = 4 − x.
Require 4 − x ≥ 0 ⇒ x ≤ 4.
Square both sides: 4x + 5 = (4 − x)^2 = x^2 − 8x + 16.
Bring to one side: x^2 − 12x + 11 = 0 → (x − 1)(x − 11) = 0.
So x = 1 or x = 11. Check in original:
- x = 1: 7 − √(4(1)+5) = 7 − 3 = 4, and 1 + 3 = 4 ✓
- x = 11: 7 − √(44+5) = 7 − 7 = 0, but 11 + 3 = 14 ✗

Only x = 1 is valid.