Question

Hi there. My professor gave my class the practice problems for our final exam. I am a little stumped on a few of them and just need someone to help jog my memory. If you have the time, could you show the steps so I can see where I went wrong and practice it. Thank you in advance, I really appreciate it.

1. 4-3(x+1)=2x
For this I got -3/5, but the answer is 1/5

2. 15x^2=x=2
Ans. 1+/-:(radical:-419) over 30 correct is -2/5,1/3

3. (:radical:4x+5)=x
ans. -5/3 correct is 5(-1 is ext)

Answer 1

4-3(x+1)=2x
4-3x-3 = 2x
4-3 = 5x
1 = 5x
x = 1/5

15x^2 + x = 2
15x^2 + x - 2 = 0
x = (-1±√(1+120))/30
= (-1±11)/30
= -12/30,10/30 = -2/5, 1/3

√(4x+5) = x
4x+5 = x^2
x^2-4x-5 = 0
(x-5)(x+1) = 0
x = -1, 5

only x=5 is a solution, since

√(-4+5) = √1 = 1, not -1
of course, squaring makes 1^2 = (-1)^2, but that is not the original equation.

Answer 2

#1
4 - 3(x+1) = 2x
4 - 3x - 3 = 2x
-5x = -1
x = -1/-5 = 1/5

#2
15x^2=x=2 , assuming you meant 15x^2 + x=2
since the = and + sign are on the same key

15x^2 + x - 2 = 0
which factors to (3x-1)(5x+2) = 0
x = 1/3 or x = -2/5
by formula: x = (-1 ± √121)/30 = 1/3 or -2/5

√(4x+5) = x
square both sides
4x+5 = x^2
x^2 - 4x - 5 = 0
(x-5)(x+1) = 0
x = 5 or x = -1
but since you squared ALL answers must be verified
if x = 5
LS = √25 = 5
RS = 5 , so that's good

if x = -1
LS = √4 = 2
RS =1 ≠LS

so x = 5