Edmundo used a number line to show the solution for the inequality |2x-6|<4 Which number line shows the solution? HURRY PLEASE
Question
Answer:
we have[tex]\left|2x-6\right|<4[/tex]Solve the inequalityFirst case[tex]+(2x-6)<4[/tex][tex]2x<4+6[/tex][tex]2x<10[/tex][tex]x<5[/tex]The solution of the first case is the interval---------> (-∞,5)All real numbers less than [tex]5[/tex]Second case[tex]-(2x-6)<4[/tex][tex]-2x<4-6[/tex][tex]-2x<-2[/tex][tex]-x<-1[/tex]------->[tex]x>1[/tex] The solution of the second case is the interval---------> (1,∞)All real numbers greater than [tex]1[/tex]The solution of the inequality [tex]\left|2x-6\right|<4[/tex](-∞,5) ∩ (1,∞)--------> [tex](1,5)[/tex]Using a graphing toolThe answer in the attached figure
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11 months ago
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