Linear Inequalities

Solving:

what do these signs mean?

(≥, ≤, >, <)

These signs represent the larger number(s) in the linear inequality, so if there is a 3x<5. this inequality would represent that 5 is larger than the 3x, another example is x≥5 this inequality represents that the x is more than or equal to 5

to solve a linear inequality you must know the correct order to do the steps, the order is BFSD, a good way to remember it is Best Friends Share Desserts, or the mathematical way Brackets Fractions Sort Divide

If we use the example of 3x+4 ≥ 12x -7 the first step would be to reduce the expression by subtracting or adding something to each side in order to get all of the x’s on one side and the numbers on the other (a lot like linear equations)

What we can do is we can take away 3x off of each x so now we are left with 4 ≥ 9x -7

as you can tell we still have to keep going because there are 2 number on one side of the sign and 1 on the other, and the whole point of these expressions is to find the value of x

the next step of this expression would be to add 7 to both of the coefficients to create yet another zero pair. Our expression is now 11 ≥ 9x. The last step would be to divide, and since the 9x is not a negative number, we do not have to flip the sign, you only do that what the x is negative.

9x/9=x  11/9= 1.2

but since this isn’t a pretty answer we could just leave it as 11≥9x

Graphing:

  

this image is showing that if the x is being poked, (like it is in image 1) that means that the line will be going to the left because the sign is opening up to the 11, not the x

but in the next example if the sign is poking the constant that means the arrow is going to the right because the x would be the bigger number.

“But when do I use a filled in do, or an open dot?”

You use the open dot when the sign does not have a small line under it, which means that the inequality is not including the number. You use a filled in dot when the sign has a small line under it, which means that that number is included in the inequality

Checking:

to check and see if you have done the inequality correctly is you replace the x in the inequality with your x equals number (answer) and you know you got the correct answer when the inequality is true based on the sign

 

 

 

images:

• https://www.varsitytutors.com/hotmath/hotmath_help/topics/graphing-inequalities-in-one-variable