how to solve inequality?

You have:

(x-1)^2 > 4

Think about a simple inequality with just numbers.

16 > 9

We have to flip the inequality sign whenever we multiply by a negative number.

-16 < -9

Now think about taking the square root of the original.

16 > 9

You get +/-4 and +/-3. The order of the +/- is important; the plusses go together, and the negatives go together. You have to flip the sign for the negatives, so you get:

4 > 3 and -4 < -3.

Note that if you didn't flip the sign, you'd have -4 > -3, which is not true. If you are confused, try simple numbers first, and that should help you understand.

Now back to the real question.

Think of equations and inequalities like a scale. If you have =, then they balance. If you have > or <, then one side is "heavier" than the other. You can add or subtract the same amount from both sides, or multiply or divide by the same (positive) quantity and the balance won't change.

There are some tricky parts. Square roots are one, as is the absolute value. These are tricky because they involve *both* signs: + and -.

Your first idea (take square root of both sides) is right. We get +/- because of the square root, and yes, we flip the sign for the negative solution. You'd take a similar approach for absolute value.

(x-1)^2 > 4
x-1 > +2 or x-1 < -2

Now we have two inequalities. We solve both.

x > 3 or x < -1

We can check. If x is 4 then 4-1=3 and 3^2=9, which is greater than 4. If x is -2 then -2-1=-3 and -3^2=9, which is again greater than 4.

Hope this helps!

square root all

x-1 > +or- 2

x > 1 +or- 2

so, you pretty much have 2 of 'em:

x > 3

and

x > -1

(x - 1)^2 > 4
x - 1 > ±√4
x - 1 > ±2

x - 1 > 2
x > 3

x - 1 > -2
x > -1

∴ -1 < x < 3

(x - 1) > 2___________(x - 1) < - 2
x > 3 _______________x < - 1

{ x : x > 3 , x < - 1, x Є R }

(x-1)^2 > 4
(x-1) > sqrt(4)
x-1 > +/- 2 read +/- plus or minus
x >1 +/- 2
x<-1 or x>3