Solve the inequality write answer in interval notation

Denote this idea with an open dot on the number line and a round parenthesis in interval notation.

Interval notation graph

Two common ways of expressing solutions to an inequality are by graphing them on a number line Solutions to an algebraic inequality expressed by shading the solution on a number line. In words, x must be less than 6 and at the same time, it must be greater than 2, much like the Venn diagram above, where Cecilia is at once breaking your heart and shaking your confidence daily. In this section you will see that some inequalities need to be simplified before their solution can be written or graphed. The parentheses indicate the boundary is not included. In the following example, you will see an example of how to solve a one-step inequality in the OR form. Interval notation requires a parenthesis to enclose infinity. Denote this with a closed dot on the number line and a square bracket in interval notation. Determine the intersection of the solutions. Solve compound inequalities in the form of and and express the solution graphically 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 this case, we have greater than zero, so we want all of the positive sections.

The number on the right should be greater than the number on the left. You will use the same properties to solve compound inequalities that you used to solve regular inequalities. Combine the solutions.

solving inequalities

To express the solution graphically, draw a number line and shade in all the values that are solutions to the inequality. If the solution set were all numbers between -2 and 3, including -2 and 3, the solution set would be written as: [-2,3].

Since the word and joins the two inequalities, the solution is the overlap of the two solutions. Graphing the inequality helps with this interpretation.

Apparently Cecilia has both of these qualities; therefore she is the intersection of the two. This is what we call a union, as mentioned above.

Note how each inequality is treated independently until the end where the solution is described in terms of both inequalities.

solve the inequality write answer in interval notation

In words, x must be less than 6 and at the same time, it must be greater than 2, much like the Venn diagram above, where Cecilia is at once breaking your heart and shaking your confidence daily. Switch the inequality if you multiply or divide by a negative number. In this case, we have less than or equal to zero, so we want the negative section.

interval notation infinity

The next example involves dividing by a negative to isolate a variable.

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Interval Notation 1