Inequalities

Symbols of Inequality

What is Inequalities?

As you can see on the image below, it indicates the Symbol and Arrow with difference direction.

The Difference between this 4 lines are only  the direction & shaded circle.

Exanples & Questions

Example 1

As you can see on the picture above it shows the final answer already which is X is greater than 3. Then you may start using the graphing inequalities. And you must point the arrow to the right because the inequalities sign '>' facing to the right.

Example 2

This example 2 shows an equation and different inequality sign that you have to solve. First thing you have to make the variable 'x' is alone, so since no 5 had the same character with number 7, you have to bring no 5 to the right side along with the plus sign but instead of plus sign, you have to changed it become minus. Then you free to solve. Plus, as you can see the inequality sign is different than before, because there's a underline. so with this inequality sign ≤
you have to shaded the circle and then you free to draw the line after you solve the problem.

Example 3

  This example 3 is a bit hard than the previous example, because as you can see there were two equation. So first thing you need to find is the like terms, once you find then you calculate as usual. But the thing is there's a  negative sign with the variable 'x'. We want to be x is alone. So bring the '-' to the right side then it will be -4. Plus as you can see the final answer the inequality sign changing its direction because of changing inequalities sign multiply or divide with a inequality sign.

Example 4

Last example is a bit confusing because the question provide 2 inequality symbol. So with this problem all you need to do is find the like term first and then calculate. after you solve everything, here's the thing there are two unshaded circle because there are 2 inequality sign, so connect the line together and make unshaded circle left and right side. And that's it.

Solve?

 Our main points is to have 'x' or  whatever the variable is with the left of inequality sign for example
x > 5 (so we called this one is final answer)

Safe Things To Do

These are things we can do without affecting the direction of the inequality:

Add (or subtract) a number from both sides
Multiply (or divide) both sides by a positive number
Simplify a side