Question

DOUBLE INEQUALITY?? Please help me solve this:
|x-1|<|x-3|

Answer 1

@Studentc14 For these squaring both sides is one method.

Example:\[\left| x +4 \right|<\left| 2x -6 \right|\]Squaring both sides yields\[x ^{2}+8x +16<4x ^{2}-24x +36\]
\[0<3x ^{2}-32x +20\]
\[3x ^{2}-32x +20>0\]
\[(3x -2)(x -10)>0\]

∴x < 2/3 or x > 10

Now you try your question and see if you understand?