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

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Operating with Inequalities: multiply & Dividing


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

Consider the adhering to examples:


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The Exception: an unfavorable Numbers

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

Whenever you main point or divide an inequality by a negative 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 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 as soon as Multiplying or splitting Variables

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


If 2x5y 10y, what is the range of potential worths for x?You cannot divide by y or 5y because 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 together it is feasible to resolve two coincided equations, so it is feasible to fix two inequalities (or three, or four, etc.). In resolving multiple simultaneously inequalities utilizing multiplication or division, the most important part is to solve each inequality separately and also then incorporate them.


If 2x 150, what is the variety of feasible values because that x?1.) resolve each inequality alone.2x x -5x x > 2 15x 150x 102.) integrate each inequality and find the overlap (i.e., the areas where each 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 whereby x 2

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

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