Inequality - A to compare of two values or expressions.For example, 10x Equation - A statement proclaiming the equality of two expressions.For example, 4x = 8 is an equation whereas 10x > 20 is an inequality.

You are watching: Why does the inequality sign flip when dividing by a negative

## Operating with Inequalities: multiply & Dividing

Performing multiplication or department with an inequality is nearly identical to multiply or splitting parts of classic equations (with one exception, extended below). ### The Exception: negative Numbers

There is one an extremely important exception to the ascendancy that multiply or separating an inequality is the same as multiplying or splitting an equation.

Whenever you multiply or division an inequality by a an unfavorable number, you must flip the inequality sign.

In the complying with example, notice how the sign as soon as the inequality is separated by -2

In the adhering to example, notification how the sign becomes a > sign once the inequality is divided by -2

-2x + 15 3-2x + 15 - 15 3 - 15-2x -12x > 6
Warning: Caution as soon as Multiplying or splitting Variables

One really important implicit of this preeminence is: girlfriend cannot divide by an unknown (i.e., a variable) uneven you room sure of its sign since you perform not recognize whether you have to flip the authorize of the inequality. There space plenty that instances wherein you will know the authorize of a variable and also as a result, you can multiply or divide and also know for sure whether you need to flip the inequality sign. However, girlfriend must constantly ask you yourself whether you recognize for certain the sign of the variable prior to dividing or multiplying when dealing with an inequality.

If 2x5y 10y, what is the range of potential worths for x?You cannot divide by y or 5y since you do not know whether y is an adverse or positive and, together such, you execute not understand whether to upper and lower reversal the inequality.

## Multiple Inequalities

Just as it is possible to solve two simultaneous equations, so the is possible to resolve two inequalities (or three, or four, etc.). In fixing multiple coincided inequalities utilizing multiplication or division, the many important component is to fix each inequality separately and then incorporate them.

If 2x 150, what is the selection of feasible values because that x?1.) solve each inequality alone.2x x -5x x > 2 15x 150x 102.) combine each inequality and also find the overlap (i.e., the areas where each inequality is satisfied--this area is the solution).x x > 2x 10The area the overlap--i.e., the equipment to the set of inequalities--is wherein x 2

For countless students, the above set of inequalities can best be taken graphically. The solution to the collection of inequalities is the overlapping graphical area.

See more: Least Common Multiples Of 9 And 12, What Do 9 And 12 Both Go Into © 2015 Lighthouse Prep, LLC. GMAT™ is a registered trademark of The Graduate administration Admission Council™ (GMAC), i beg your pardon does no endorse no one is affiliated in any way with the owner of this website or any content included herein. All contents (including practice questions and study guides) is created by PlatinumPrep, LLC no GMAC.