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

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## Operating v Inequalities: multiplying & Dividing

Performing multiplication or division with one inequality is nearly identical to multiply or splitting parts of traditional equations (with one exception, spanned below). ### The Exception: negative Numbers

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

Whenever you main point or divide an inequality by a an adverse number, you should flip the inequality sign.

In the adhering to example, notice how the sign as soon as the inequality is separated by -2

In the complying with example, an alert how the authorize becomes a > sign as soon as 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 very important implicit of this preeminence is: friend cannot division by one unknown (i.e., a variable) uneven you are sure of its sign because you do not know whether you must flip the sign of the inequality. There room plenty of instances wherein you will know the authorize of a variable and also as a result, you can multiply or divide and know for certain whether you have to flip the inequality sign. However, girlfriend 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 variety of potential values for x?You cannot division by y or 5y because you perform not recognize whether y is an unfavorable or hopeful and, as such, you execute not understand whether to flip the inequality.

## Multiple Inequalities

Just together it is possible to settle two simultaneously equations, so the is feasible to solve two inequalities (or three, or four, etc.). In resolving multiple coincided inequalities using multiplication or division, the most important part is to solve each inequality separately and also then incorporate them.

If 2x 150, what is the range of feasible values for x?1.) settle 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 that overlap--i.e., the systems to the collection of inequalities--is wherein x 2

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

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