Question

Complete the statement: if |2x-1|<2 and |3-x|<5 then:
Can you please explain each step please? I have a a lot more of these types of questions and I dunno how to do them.

Answer 1

if \(|2x-1|<2\) then
\[-2<2x-1<2\\
-1<2x<3\\
-\frac{1}{2}<x<\frac{3}{2}\]

Answer 2

I forgot to say but there are answer choices:
A. \[\left| x-\frac{ 1 }{ 2 } \right|<1\]
B. \[\left| 3x-4 \right|<7\]
C. \[\left| x-\frac{ 1 }{ 2 } \right|>1\]
D.\[\left| x-4 \right|>1\]
E.\[\left| x-4 \right|<1\]

Answer 3

\(|2x-1| \lt 2\)
divide by 2:

\(\Large \frac{|2x-1|}{2} \lt \frac 22\)
\(\Large |x-\frac 12|\lt 1\)

Answer 4

But how about the second inequality? What do I do with |3-x|<5 ?