Inequalities

• There is one critical difference between equations and inequalities:
•  When dividing or multiplying an inequality by a negative number, the inequality sign must alwaysbe flipped!

Also note that you should never multiply or divide an inequality by a variable! Unless you know whether that variable represents a positive or negative number, you do not know whether to flip the sign!

Always consider the positive and the negative scenarios when dividing or multiplying an inequality by a variable whose value you don’t know!

• Be careful, however, when dividing or multiplying an inequality by a variable (or a combination of variables) whose value you don’t know! Because you don’t know whether the variable is positive or negative, you don’t know whether to flip the sign.
• ‘Ifad >bd,isa >b?’

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