Question

If m is an integer and $|2m-2|<1$, find the value of $m$.

• A. $-2$
• B. $-1$
• C. $0$
• D. $1$

Answer 1

The correct option is D $1$

$|2m-2|<1$

Squaring both of side

$4m^2-8m+4<1$

$\Rightarrow$ $4m^2-8m+3<0$

Now factorize the quadratic

$\Rightarrow$ $(2m-1)(2m-3)<0$

$\Rightarrow$ $mϵ(\frac{1}{2},\frac{3}{2})$

$m$ is an integer so the only possible value of $m$ is $1$

$\Rightarrow$ $m=1$

Hence, option D is correct.