Table of Contents
How do you write a solution set of a compound inequality?
The graph of a compound inequality with an “and” represents the intersection of the graph of the inequalities. A number is a solution to the compound inequality if the number is a solution to both inequalities. It can either be written as x > -1 and x < 2 or as -1 < x < 2.
What is a solution set in compound inequalities?
The solution of a compound inequality that consists of two inequalities joined with the word and is the intersection of the solutions of each inequality. In other words, both statements must be true at the same time.
How do you write all solution sets?
The set containing all the solutions of an equation is called the solution set for that equation. If an equation has no solutions, we write ∅ for the solution set. ∅ means the null set (or empty set)….Solution Sets for Equations.
| Equation | Solution Set |
|---|---|
| x+1=x | ∅ (the empty set) |
When solving a compound inequality containing the word and the solution set is the?
This makes it easier to distinguish between the two types of inequalities. The solution to a compound inequality containing the word “or” is the union of the solution sets. This means that the solution sets will not overlap or intersect.
What is the solution to the inequality?
A solution for an inequality in x is a number such that when we substitute that number for x we have a true statement. So, 4 is a solution for example 1, while 8 is not. The solution set of an inequality is the set of all solutions.
How do you tell if it is an AND or OR inequality?
If it is a conjunction that uses the word and, the solution must work in both inequalities and the solution is in the overlap region of the graph. If it is a disjunction that uses the word or, the solution must work in either one of the equations.
How do you solve a compound inequality?
Compound inequalities are solved by isolating your variable on one side of the inequality. If the components are connected by “and,” the variable is located between the two constraining values.
How do you graph a compound inequality?
Graphing Compound Inequalities. When graphing compound inequalities on a line, draw a circle (for > or < inequalities) or dot (for ≥ or ≤ inequalities) at the bound points, or the values you know in the inequalities, to begin your graph. If graphing an “and” inequality, draw a line between the two bound points to complete the graph.
How do you calculate an inequality?
Plug your slope and a point into the formula y = mx + B, in which “m” is the slope, (x, y) is a point on the line and “b” is the y-intercept, to find the equation governing the inequality line. Plugging in (0, 0), you obtain 0 = 0 + b, so b = 0. Rewriting the equation, you obtain y = x/2.
What is compound inequality?
A compound inequality is a statement in which two inequalities are connected by the word “and” or the word “or”.