**Basic linear Inequalities**

**(single variable)**

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Not all statements in mathematics involve managing equal quantities. Sometimes, we might only recognize that other is "greater than" a particular value, or "less 보다 or same to" another value. These cases are described as **inequalities** (because they are not just "equal").

a b ; a is greater than or same to b

a b ; a is much less than or equal to b

If you can solve a straight equation, you have the right to solve a linear inequality. The process is the same, v one vital exception ...

You are watching: Is less than or equal to an open circle

... As soon as you multiply (or divide) an inequality by a negative value, you must readjust the direction the the inequality.

We know that 3 is much less than 7. Now, allows multiply both political parties by -1. Research the outcomes (the products).

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top top a number line, -3 is come the ideal of -7, making -3 better than -7. -3

**>**-7 We need to reverse the direction that the inequality, when we main point by a negative value, in order to preserve a "true" statement.

When graphing a straight inequality top top a number line, usage an

**open circle**because that

*"less than"*or

*"greater than"*, and also a

**closed circle**because that

*"less than or equal to"*or

*"greater than or equal to"*.

To **CHECK** one inequaltiy, that is not feasible to test every value. So inspect a value in every *shaded region* to view if that is TRUE. Then inspect a value in every *non-shaded region* to see if that is FALSE.

The solution collection for this difficulty will it is in all values that room graphed come the right the -3, and also including -3. CHECK: A number in the shaded an ar = TRUE. A number in the non-shaded area = FALSE. Choose 0: 0 > -3 TRUE Pixk -4: -4 > -3 FALSE Graph the solution collection of: x |