Set builder and interval notation worksheet pdf

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Set builder and interval notation worksheet pdf

Learning Objectives (1.1.1) ? Represent inequalities on a number line (1.1.2) ? Graphing an Inequality (1.1.3) ? Represent inequalities using interval notation (1.1.4) ? Set-builder notation Sometimes there is a range of possible values to describe a situation. When you see a sign that says "Speed Limit 25," you know that it doesn't mean that you have to drive exactly at a speed of 25 miles per hour (mph). This sign means that you are not supposed to go faster than 25 mph, but there are many legal speeds you could drive, such as 22 mph, 24.5 mph or 19 mph. In a situation like this, which has more than one acceptable value, inequalities are used to represent the situation rather than equations. Solving multi-step inequalities is very similar to solving equations--what you do to one side you need to do to the other side in order to maintain the "balance" of the inequality. The Properties of Inequality can help you understand how to add, subtract, multiply, or divide within an inequality. (1.1.1) ? Represent inequalities on a number line First, let's define some important terminology. An inequality is a mathematical statement that compares two expressions using the ideas of greater than or less than. Special symbols are used in these statements. When you read an inequality, read it from left to right--just like reading text on a page. In algebra, inequalities are used to describe large sets of solutions. Sometimes there are an infinite amount of numbers that will satisfy an inequality, so rather than try to list off an infinite amount of numbers, we have developed some ways to describe very large lists in succinct ways. The first way you are probably familiar with--the basic inequality. For example: [latex]{x}\lt{9}[/latex] indicates the list of numbers that are less than 9. Would you rather write [latex]{x}\lt{9}[/latex] or try to list all the possible numbers that are less than 9? (hopefully, your answer is no) [latex]-5\le{t}[/latex] indicates all the numbers that are greater than or equal to [latex]-5[/latex]. Note how placing the variable on the left or right of the inequality sign can change whether you are looking for greater than or less than. For example: [latex]x\lt5[/latex] means all the real numbers that are less than 5, whereas; [latex]5\lt{x}[/latex] means that 5 is less than x, or we could rewrite this with the x on the left: [latex]x\gt{5}[/latex] note how the inequality is still pointing the same direction relative to x. This statement represents all the real numbers that are greater than 5, which is easier to interpret than 5 is less than x. The second way is with a graph using the number line: And the third way is with an interval. We will explore the second and third ways in depth in this section. Again, those three ways to write solutions to inequalities are: an inequality an interval a graph Inequality Signs The box below shows the symbol, meaning, and an example for each inequality sign. Sometimes it's easy to get tangled up in inequalities, just remember to read them from left to right. Symbol Words Example [latex]eq [/latex] not equal to [latex]{2}eq{8}[/latex], 2 is not equal to 8. [latex]\gt[/latex] greater than [latex] {5}\gt{1}[/latex], 5 is greater than 1 [latex]\lt[/latex] less than [latex]{2}\lt{11}[/latex], 2 is less than 11 [latex] \geq [/latex] greater than or equal to [latex]{4}\geq{ 4}[/latex], 4 is greater than or equal to 4 [latex]\leq [/latex] less than or equal to [latex]{7}\leq{9}[/latex], 7 is less than or equal to 9 The inequality [latex]x>y[/latex] can also be written as [latex]{y}) or less than (

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