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

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Operating v Inequalities: multiplying & Dividing

Performing multiplication or department with one inequality is nearly identical to multiply or separating parts of traditional equations (with one exception, covered below).

Consider the complying with examples:


The Exception: an adverse Numbers

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

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

In the following example, notice how the sign once the inequality is split by -2

In the complying with example, notification how the sign becomes a > sign as soon as the inequality is divided by -2

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

One really important implicit of this dominance is: friend cannot division by one unknown (i.e., a variable) unless you are sure the its sign since you execute not recognize whether you need to flip the sign of the inequality. There room plenty that instances wherein you will understand the authorize of a variable and as a result, you have the right to multiply or divide and also know for certain whether you should flip the inequality sign. However, friend must constantly ask yourself whether you know 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 values for x?You cannot division by y or 5y because you do not understand whether y is an unfavorable or positive and, together such, you do not know whether to upper and lower reversal the inequality.

Multiple Inequalities

Just together it is possible to deal with two simultaneous equations, so that is possible to resolve two inequalities (or three, or four, etc.). In fixing multiple coincided inequalities using multiplication or division, the many important component is to deal with each inequality separately and also then combine them.

If 2x 150, what is the selection of feasible values for x?1.) fix each inequality alone.2x x -5x x > 2 15x 150x 102.) integrate 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 of overlap--i.e., the equipment to the collection of inequalities--is where x 2

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

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