Can anyone help me answer these questions? I just really suck at inequalities and don't know how to answer these. Please help?
1.Explain why and when you need to switch the inequality sign when solving an inequality.
2.How can you tell which direction to shade the graph of an inequality?
3.What is the difference between graphing conjunctions and disjunctions?
4.What is one difference between an inequality with one variable and one with two variables?
5.How do “closed and open circles” relate to “dashed and solid lines”?
Stacey Warren - Expert brainly.com
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I'm not going to do all 5. I'm only doing one.
That's fine. I'll take all the help I can get.
Alright, next time, post one question at at time, not five in a question.
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Let's say we have:
\[-a>b\]If we rearrange the equation we get:
\[0>b-a\]And if we rearrange again we get:\[-b>a\] or \[a<-b\]So, when do swap the inequality? Do you know?
when it's only a negative
Negative and when we are multiplying and dividing. This is something you just have to memorize.
|dw:1356903237059:dw|open circle means the number is not include and dashed line means the numbers on the line are not included
solid circle means the number is included and solid line means the numbers are included
|dw:1356903359427:dw|3 in not a solution but any number bigger than 3 is (example 3.1, 3.2, 4, 5, 100, etc)
|dw:1356903434970:dw|now 3 is also part of the solution
|dw:1356903467129:dw|only the area under the dotted line is the solution
|dw:1356903509899:dw|now the line is also part of the solution
There are rules for inequalities and once you learn these, you will be answering others peoples questions about how to do them.
Rule one ...Adding or subtracting the same number on both sides, even if the numbers are negative, WILL NOT change the sign.
Rule two ...Multiplying and dividing by a POSITIVE number, WILL NOT change the sign.
Rule three ...Multiplying and dividing by a NEGATIVE number, WILL change the sign.
Rule 4 ...When switching the different sides, you WILL change the signs.
example : x > 1 is also 1 < x
Which direction to shade the graph ..
When y is less then, you shade below the line, and when y is greater then, you shade above the line.
If x is less then, you shade to the right of the line, and when x is greater then, you shade to the left of the line.
conjunction - contains the word "and" . Is true if both inequalities are true
disjunction - contains the word " or ". Only one of the inequalities is true.
A conjunction is the combination of two inequalities on a number line.
example : x > 0 and 3 > x can be written as 0 < x < 3
when graphing this....your number line is 0 - 3...you have open circles on 0 and 3 with everything shaded in between.
A disjunction is going to have two inequalities on the same number line.
example : x <1 or x > 3
when graphing this .....lets make your number line from 0 - 4...you have an open circle on 1 shaded to the left and an open circle on 3 shaded to the right.
An open circle means that the number is not part of the solution.
example : x < 3 : x > 5....neither of these inequalities are going to have closed circles because the 3 and the 5 are not part of the solution.
A closed circle means that the number is part of the solution.
example : x >= 4 (greater then or equal)
This one would have a closed circle because 4 is part of the solution. If there is an equal sign, then the number is part of the solution.
Dashed line means numbers on the line are not included.
Solid line means the numbers on the line are included.