Bell Work: Simplify -6 -2. Answer: -1/36 Lesson 37: Inequalities, Greater Than and Less Than, Graphical Solutions of Inequalities.

Bell Work:Simplify -6

-2

Answer:-1/36

Lesson 37:Inequalities, Greater Than and Less Than, Graphical Solutions of Inequalities

We use symbols≠ > <

To designate that quantities are not equal, and we say that these symbols are symbols of inequality. They can be read from left to right or from right to left.

We read 4 ≠ 5From left to right as “4 is not equal to 5”, or from right to left as “5 is not equal to 4”.

The symbols > and < are inequality symbols and are also called greater than/less than symbols. When we read, we read only one end of the symbol, the end that we come to first.

Thus we read 4 > 2From left to right as “4 is greater than 2”, or from right to left as “2 is less than 4”.

If the sign is combined with an equal sign, only one of the conditions must be met. We read

4 ≥ 2 + 2From left to right as “4 is greater than or equal to 2 plus 2”, or from right to left as “2 plus 2 is less than or equal to 4”. This combination symbol is also called an inequality symbol although half of it is an equal sign.

Inequalities can be false inequalities, true inequalities, or conditional inequalities.

4 + 2 ≤ 3False inequalityx + 2 ≥ xTrue inequalityx < 4Conditional because it depends on the replacement value used for the variable.

If a number that we use as a replacement for the variable makes the inequality a true inequality, we say that the number is a solution of the inequality and say that the number satisfies the inequality.

If the number that we use as a replace for the variable makes the inequality a false inequality, then the number is not a solution of the inequality and does not satisfy the inequality. Since more than one number will often satisfy a given inequality, there is often more than one solution to the inequality.

We call the set of numbers that will satisfy a given equation or inequality the solution set of the equation or inequality.

Greater than and Less than:Zero is a real number and can used to describe a distance of zero. Any other number that can be used to describe a physical distance is a positive real number, and the opposite of each of these numbers is a negative real number.

We use the number line to help us picture the way real numbers are ordered (arranged in order) and to help us define what we mean by greater than. On this number line we have graphed 2 and 4.

We remember that one number is greater than another number if its graph is to the right of the graph of the other number. Since the graph of 4 is to the right of the graph of 2, we say that 4 is greater than 2.

Using the same definition, we can say that -1 is greater than -4 because the graph of -1 is to the right of the graph of -4.

Graphical Solutions of Inequalities:We can use a number line to display the graph of the picture of the solution to many problems.

Example:Draw a number line and graph the solution of x > 2.

Answer:The open circle indicates that 2 is not part of the solution.

Example:Draw a number line and graph the solution of x ≤ 2.

Answer:The solid circle indicates that the number 2 is a part of the solution.

Example:Write an inequality that describes this graph.

Answer:x < -3

HW: Lesson 37 #1-30