Physicsissuef said:Because you have two possible solutions for (x+5)(x+3)>0
the first one:
x+5>0 ; x>-5
x+3>0 ; x>-3
[tex](-5, +\propto) \cap (-3, +\propto) = (-3, +\propto)[/tex]
and the second
x+5<0 ; x<-5
x+3<0 ; x<-3
[tex](-\propto, -5) \cap (-\propto, -3) = (-\propto, -5) [/tex]
The final solution:
[tex](-\propto, -5) \cup (-3, +\propto)[/tex]
Anyway, this way is much more time-consuming... So you shouldn't use it in future.. There is much easier way...
An inequality is a mathematical statement that compares two quantities using symbols such as <, >, ≤, or ≥. It shows that one quantity is greater or less than the other.
Solving inequalities by factoring allows us to find the values or range of values that make the inequality true. This is especially useful when working with equations that involve variables or unknown values.
Factoring is the process of breaking down a polynomial or algebraic expression into smaller parts that can be easily multiplied to obtain the original expression. In the context of inequalities, factoring helps us find the values that satisfy the inequality by simplifying the expression.
To solve an inequality by factoring, first set the expression equal to 0. Then, factor the expression into smaller parts. Next, use the Zero Product Property to find the values that make each factor equal to 0. Finally, use a number line to plot the solutions and determine the final solution set.
Yes, for example, to solve the inequality x^2 + 3x - 10 > 0, we first set it equal to 0: x^2 + 3x - 10 = 0. Then, we factor the expression into (x+5)(x-2) = 0. Using the Zero Product Property, we find that x = -5 or x = 2. We plot these values on a number line and see that the solution set is x < -5 or x > 2. Therefore, the inequality is true when x is either less than -5 or greater than 2.