CHAPTER 3 PROJECT

SECTION 3.1

• When you want to find what number makes the inequality true, you plug in that number in the place of the variable.
• When you graph an inequality you put an arrow the direction it is and an open dot for greater or less than and a closed dot for greater than or equal to and less than or equal to.

THESE ARE INEQUALITIES

GRAPHS LOOK LIKE THIS

SECTION 3.2

• You sometimes have to add or subtract in inequalities, like in equations.
• When you add or subtract in an inequality you do it to both sides of the inequality the left side and the right side.
• In an inequality your main goal is to isolate the variable. You do that by doing the opposite operation, if it adds you subtract and vice versa.

SECTION 3.3

• When solving inequalities you sometimes have to multiply or divide.
• You still have to do the opposite operations to isolate the variable.
• If you multiply or divide by a negative number you have to flip the sign.
• So if it's greater than you change it to less than and vice versa.

REMEMBER TO FLIP THE SIGN WHEN YOU MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER

SECTION 3.4

• Sometimes you need to do more than one step to isolate the variable and solve the inequality.
• It is easy as long as you remember:
• 1.) Isolate the variable using opposite operations.
• 2.) Flip the sign when you multiply or divide by a negative number.
• 3.) Whenever you do an operation do it to the left and the right.
• 4.) If you add a number to a side and its subtracting the number, then both the numbers cancel out.

SECTION 3.6

• A compound inequality involves a value that is between two numbers.
• You need 2 inequality signs for a compound inequality.
• If x is less than 3 but more than 1 that means x could be any number between 1 and 3, such as 1.1, 2.4, or even 2.99.
• They are separated in interval notation by and/or.
• On a graph if you want to show a number is between 2 numbers using greater than or less than you draw an open dot from the first number to the second number , which will also be an open dot.

INTERVAL NOTATION - AND/OR

• Interval notation is when you display a graph in the form of brackets.
• The curved bracket shows that the number is not included or open. The straight bracket shows that the number is included or closed.
• For compound inequalities you need to draw 2 interval notations and separate them with AND.
• In an absolute value equation or inequality you say x =? OR x= - ?

SECTION 3.7

• Sometimes there is an object and you can be 1 meter away on the left side or 1 meter away on the right side.
• You can show this using absolute value.
• Absolute value is the amount of units between a number and 0.
• A positive number's absolute value is the same as the absolute value of the negative form of that number.
• The absolute value of 3 is 3 and the absolute value of -3 is also 3 because both are 3 spaces from 0.
• In an absolute value equation or inequality you still have to isolate the variable to get your answer

HOW TO SOLVE INEQUALITY WORD PROBLEMS

• In an inequality word problem you can put the variable anywhere you like but the sign must still make sense.
• You need to figure out which values go on the right side and which values go on the left side.
• Then you solve the inequality and isolate the variable.
• In some word problems you might use addition, in some subtraction, in some multiplication, in some division, and in others absolute value.

THE END