a) Solve the following inequation and represent the solution set on the number line : 2x−5≤5x+4<11,wherexϵI
b) Solve the following inequation and represent the solution set on the number line ? −3<−12−2x3≤56,xϵR
[6 MARKS]
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Solution
Each subpart: 3 Marks
a) 2x−5≤5x+4and5x+4<11,xϵI⇒−9≤3xand5x<7⇒−3≤xandx<75⇒{−3≤x<75,xϵI}Solutionset={−3,−2,,−1,0,1} b) Given:−3<−12−2x3≤56,xϵR.⇒−18<3−4x≤56⇒−15<−4x;−4x≤8⇒x<154;x≥−2⇒x<3.75;x≥−2Solutionset={−2≤x<3.75,xϵR}