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Sagot :
we have the inequality
[tex]|2x-2|+4>12[/tex]solve for x
subtract 4 both sides
[tex]\begin{gathered} |2x-2|+4-4>12-4 \\ |2x-2|>8 \end{gathered}[/tex]step 1
Find the first solution (positive case)
[tex]\begin{gathered} +(2x-2)>8 \\ 2x\text{ >8+2} \\ 2x\text{ > 10} \\ x>5 \end{gathered}[/tex]the solution of the first case is the interval (5, infinite)
step 2
Find the second solution (negative case)
[tex]\begin{gathered} -(2x-2)>8 \\ mu\text{ltiply by -1 both sides} \\ 2x-2\text{ <-8} \\ 2x<\text{ -8+2} \\ 2x<-6 \\ x<-3 \end{gathered}[/tex]the second solution is the interval (-infinite, -3)
(-infinite, -3) ∩ (5, infinite)
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