Question

I need some help please

Answer 1

we have the inequality

$\mleft|2x-9\mright|<2$

step 1

Find out the first solution (positive case)

$\begin{gathered} +(2x-9)<2 \\ 2x<2+9 \\ 2x<11 \\ x<5.5 \end{gathered}$

the first solution is the interval (-infinite, 5.5)

step 2

Find out tye second solution (negative case)

$\begin{gathered} -(2x-9)<2 \\ mu\text{ltiply by -1 both sides} \\ 2x-9>-2 \\ 2x>\text{ -2+9} \\ 2x>7 \\ x>3.5 \end{gathered}$

the second solution is the interval (3.5, infinite)

step 3

Find out the total solution

the solution is

(-infinite, 5.5) ∩ (3.5, infinite)=(3.5,5.5)

the solution is the interval (3.5,5.5)