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

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## Operating v Inequalities: multiply & Dividing

Performing multiplication or division with one inequality is practically identical to multiplying or separating parts of traditional equations (with one exception, covered below).

### The Exception: an adverse Numbers

There is one really important exemption to the ascendancy that multiplying or splitting an inequality is the very same as multiplying or separating an equation.

Whenever you multiply or divide an inequality through a an unfavorable number, you have to flip the inequality sign.

In the adhering to example, notification how the sign once the inequality is split by -2

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

-2x + 15 3-2x + 15 - 15 3 - 15-2x -12x > 6
Warning: Caution once Multiplying or dividing Variables

One really important implicit of this ascendancy is: girlfriend cannot divide by an unknown (i.e., a variable) uneven you are sure the its sign because you do not know whether you must flip the authorize of the inequality. There room plenty that instances wherein you will recognize the sign of a variable and also as a result, you have the right to multiply or divide and also know for certain whether you must flip the inequality sign. However, you must constantly ask you yourself whether you understand for sure the sign of the variable before dividing or multiply when taking care of an inequality.

If 2x5y 10y, what is the variety of potential worths for x?You cannot divide by y or 5y since you do not recognize whether y is negative or optimistic and, together such, you execute not know whether to flip the inequality.

## Multiple Inequalities

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

If 2x 150, what is the range of possible values because that x?1.) solve each inequality alone.2x x -5x x > 2 15x 150x 102.) combine 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 solution to the collection of inequalities--is whereby x 2

For numerous students, the above collection of inequalities can finest be understood graphically. The equipment to the collection of inequalities is the overlapping graphical area.

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