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Remember: Flip the Sign! –
- 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!
Multiplying and dividing unknown variables
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?’
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