Combining Inequalities –
Many problems that contains two or more inequalities can be simplified by combining the inequalities.
To combine inequalities, simplify each inequality so that all the inequality signs point in the same direction and stack them.
‘Ifx –4<8,x +5>6,andx +2>5,whatarethepossiblevaluesofx?’
Answer: 3<x<12. Ifx–4<8,thenx<12. Likewise,ifx+5>6,thenx>1. Finally,ifx+2>5,thenx> 3. Arranging all three inequalities in the same direction reveals that:x < 12 1<x3<x x 3 < x < 12