Question

Solve (2x-2)(x-2)=1-x by factorization​

Answer 1

Answer:

x is 2

Step-by-step explanation:

(2x-2)(x-2)=1-x

$\frac{-2(1 -x)(x - 2)}{(1 - x)} = 0$

$\frac{-2(x - 2)}{1} = 0$

-2x + 4 = 0

2x = 4

x = 4/2

x = 2

Answer 2

Step-by-step explanation:

Given:-

(2x-2)(x-2)=1-x

To find:-

Solve (2x-2)(x-2)=1-x by factorization

Solution:-

Given equation is (2x-2)(x-2)=1-x

=> (2x-2)(x-2)-1+x = 0

=> 2(x-1)(x-2)-(1-x) = 0

=> 2(x-1)(x-2)+(x-1) = 0

=> (x-1) [2(x-2)+1] = 0

=>(x-1)(2x-4+1) = 0

=>(x-1)(2x-3) = 0

=>(x-1) = 0 or (2x-3) = 0

=>x = 1 or 2x=3

=>x = 1 or x = 3/2

Answer:-

The solutions for the given problem are 1 and 3/2

Check:-

If x = 1 then

LHS = (2×1-2)(1-2)

=>(2-2)(-1)

=>0

RHS = 1-1= 0

LHS = RHS is true for x= 1

If x=3/2 then

LHS= [(2×3/2)-2][(3/2)-2]

=>(3-2)[(3-4)/2]

=>(1)(-1)/2

=>-1/2

RHS= 1-(3/2)

=>(2-3)/2

=>-1/2

LHS=RHS is true for x = 3/2

Used method:-

• Factorization method