Nitrate said:Homework Statement
Solve x/(x-2) > 2 by first rewriting it in the form P(x)/Q(x)>0
Homework Equations
The Attempt at a Solution
well... i got up to
x/(x - 2) > 2
x/(x - 2) - 2 > 0
x/(x - 2) - 2(x - 2)/(x - 2) > 0
x/(x - 2) - (2x - 4)/(x - 2) > 0
(x - 2x + 4)/(x - 2) > 0
(-x + 4)/(x - 2) > 0
-x + 4 > 0 and x - 2 > 0 OR -x + 4 < 0 and x - 2 < 0
However, i do not understand why there has to be an OR case if the inequality is only >
please help :)
Mark44 said:Because numerator and denominator are either both positive OR both negative.
An inequality is a mathematical statement that compares two quantities or expressions and shows their relative sizes. It uses symbols such as <, >, ≤, and ≥ to represent the relationship between the two quantities.
To solve an inequality, you need to isolate the variable on one side of the inequality sign. This can be done by using inverse operations, similar to solving an equation. However, when multiplying or dividing both sides by a negative number, the inequality sign must be flipped.
Yes, inequalities can be graphed on a number line or a coordinate plane. The solution to an inequality is represented by a shaded region on the graph, depending on the type of inequality and whether the solution includes or excludes certain values.
A linear inequality contains a variable raised to the first power, while a quadratic inequality contains a variable raised to the second power. This means that the graph of a linear inequality is a straight line, while the graph of a quadratic inequality is a curve.
Yes, compound inequalities are inequalities that contain more than one inequality statement. When solving these, it is important to consider the relationship between the two inequalities and use the correct combination of solutions. For example, if the two inequalities are joined by "and", the solution must satisfy both inequalities, while if they are joined by "or", the solution can satisfy either one of the inequalities.