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

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Operating v Inequalities: multiply & Dividing

Performing multiplication or department with an inequality is virtually identical to multiplying or splitting parts of timeless equations (with one exception, extended below).

Consider the following examples:


The Exception: negative Numbers

There is one an extremely important exception to the preeminence that multiplying or separating an inequality is the exact same as multiplying or dividing an equation.

Whenever you multiply or divide an inequality by a negative number, you should flip the inequality sign.

In the following example, notification how the sign as soon as the inequality is split by -2

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

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

One very important implicit of this preeminence is: girlfriend cannot division by one unknown (i.e., a variable) unless you space sure the its sign because you execute not know whether you should flip the authorize of the inequality. There room plenty of instances whereby you will recognize the authorize of a variable and as a result, you have the right to multiply or divide and know for certain whether you must flip the inequality sign. However, you must always ask yourself whether you understand for certain the sign of the variable prior to dividing or multiply when handling an inequality.

If 2x5y 10y, what is the range of potential worths for x?You cannot division by y or 5y because you execute not know whether y is negative or confident and, as such, you perform not understand whether to flip the inequality.

Multiple Inequalities

Just together it is feasible to solve two coincided equations, so that is feasible to settle two inequalities (or three, or four, etc.). In resolving multiple simultaneous inequalities making use of multiplication or division, the many important part is to solve each inequality separately and also then integrate them.

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

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

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