ONE-STEP INEQUALITIES

What to do when graphing inequalities.

- if x is less then something then put a empty circle on the number and go left on the number line. - When x is equal or less then a number then put a filled in circle on the number and go left on the numberline.

Remember

Again, when we divided by a positive number, we still got a true statement. But, when we divided by a negative number, we got a false statement. Negative 2 is not less than -3. When we used negative numbers to multiply and divide, our results were not true statements. But, we can fix this! All we have to do is switch the inequality symbol around to make these statements true! Everything else is the same as solving equations.

Be Careful!

Don't make the mistake of starting at the next integer on the number line, and then shading. For example, if we put a circle on the 4 in this problem, we wouldn't be including all of the decimal values between 4 and 5.

RULE

If you multiply or divide by a negative number, flip the inequality symbol around to make the sentence true.

Before continuing, make sure you understand the main points of this lesson.

Inequalities can be used to describe situations where there is more than one solution. When multiplying or dividing an inequality by a negative number, flip the inequality sign around. On a graph, a closed circle indicates that the border value is included, and an open circle indicates that the border value isn't included. Carefully read the inequality to make sure you shade in the right direction. Shaded numbers must make the inequality statement true.

Before continuing, make sure you understand the main points of this lesson.

Two-step inequalities are solved in the same way as two-step equations—by working backward. When you multiply or divide an inequality by a negative number, reverse the inequality symbol. The solution set of an inequality can be represented using a number line.

closed circle

a circle filled in to show that the point is a part of the solution set

open circle

a circle not filled in to show that the point is a border value and is not included as part of the solution set

when putting solutions in the comparision if you:

add, subtract, divide, a negative with a postive your most likely to get a false answer. Example: 4 < 6 4 ÷ (-2) < 6 ÷ (-2) -2 < -3 <- See -3 is not greater than -2.

infinite

increasing or decreasing without end

inequality

sentence showing a relationship between numbers or expressions that are not necessarily equal; uses the symbols >, <, ≥, ≤, or ≠

solution

the value(s) of a variable that will make a mathematical statement true