InequalitiesDate: 01/24/2001 at 22:08:56 From: Nick Kincannon Subject: Pre-Algebra How do you add, subtract, multiply, and divide inequalities? Date: 01/26/2001 at 13:18:47 From: Doctor Alicia Subject: Re: Pre-Algebra Hi Nick, When you add, subtract, multiply, and divide inequalities, you treat the inequality as if it were an equation (=). You flip the inequality if you divide or multiply by a negative number. For example: 7 + 2x > 12 Subtract 7 from both sides: 7 - 7 + 2x > 12 - 7 2x > 5 Divide both sides by 2 but keep the inequality symbol as-is: 2x > 5 --- --- 2 2 x > 5 --- 2 Therefore, x is greater than 5/2. To check our work, pick any x greater than 5/2, such as 7/2. 7 + 2 * 7 > 12 --- 2 The 2's cancel out: 7 + 7 > 12 14 > 12 So we see that our inequality holds true. Now, let's try the a similar problem but one dealing with multiplying or dividing negative numbers: 7 - 2x > 12 Subtract 7 from both sides: 7 - 7 - 2x > 12 - 7 - 2x > 5 Divide by *negative* 2 and flip the inequality: - 2x < 5 --- --- - 2 -2 The -2's cancel out: x < -5 --- 2 Therefore, x is less than -5/2. To check our work, pick a number less than -5/2, such as -10. 7 - 2(-10) > 12 7 + 20 > 12 27 > 12 We see that the inequality holds true. I hope this helps. Write back if you have any further questions. - Doctor Alicia, The Math Forum http://mathforum.org/dr.math/ |
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