Inequality - A comparison of 2 values or expressions.For example, 10x Equation - A statement heralding the equality of 2 expressions.For example, 4x = 8 is an equation vice versa, 10x > 20 is an inequality.

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Operating v Inequalities: multiply & Dividing

Performing multiplication or division with one inequality is almost identical to multiply or separating parts of traditional equations (with one exception, extended below).

Consider the complying with examples:


The Exception: an adverse Numbers

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

Whenever you main point or division an inequality through a an unfavorable number, you need to flip the inequality sign.

In the following example, notice how the sign when the inequality is divided by -2

In the following example, notice how the sign becomes a > sign when the inequality is split by -2

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

One an extremely important implication of this dominance is: girlfriend cannot division by one unknown (i.e., a variable) unless you are sure of its sign because you carry out not understand whether you need to flip the sign of the inequality. There are plenty that instances whereby you will know the authorize of a variable and also as a result, you have the right to multiply or divide and also know for sure whether you should flip the inequality sign. However, girlfriend must constantly ask yourself whether you understand for certain the authorize of the variable prior to dividing or multiplying when managing an inequality.

If 2x5y 10y, what is the range of potential worths for x?You cannot divide by y or 5y since you perform not recognize whether y is negative or hopeful and, as such, you execute not know whether to upper and lower reversal the inequality.

Multiple Inequalities

Just as it is feasible to resolve two coincided equations, so that is possible to resolve two inequalities (or three, or four, etc.). In resolving multiple coincided inequalities making use of multiplication or division, the most important component is to solve each inequality separately and then incorporate them.

If 2x 150, what is the variety of possible values because that x?1.) fix each inequality alone.2x x -5x x > 2 15x 150x 102.) incorporate each inequality and find the overlap (i.e., the areas where every inequality is satisfied--this area is the solution).x x > 2x 10The area that overlap--i.e., the systems to the collection of inequalities--is wherein x 2

For many students, the above collection of inequalities can ideal be interpreted graphically. The solution to the set of inequalities is the overlapping graphical area.

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