Jason Solves Inequalities

Jason Solves It!Inequalities with

Multiplication & Division

that’s me

6Y + 2 < 38

Click for

answer

-4x – 8 > 8

x + 4 < -731

An inequality is the relation between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”

variable

< 38

Just like in an equation, when trying to solve an inequality, you need to isolate

the variable.

It just means you gotta get the variable on a side all by itself. In this inequality, it’s going to take more than one step.

6Y+2

Click here for answer


Y < some number

A variable is a letter or symbol that represents a value…

Well, to get rid of that 2 on the left side of the inequality, we subtract 2 from both sides.

< 38

6Y + 2Click here to

continue

The “- 2” on the left side of the inequality cancels out the “+

2” on the left side. On the right side of the inequality, you just subtract 2 from 38,

which is 36.


< 38

6Y+2

- 2

- 2

- 2

- 2< 36

A linear inequality in one variable is an inequality (1 variable) that can be written in the form ax + b < 0 or ax + b > 0, where a & b are real numbers and a ≠0.


Right now, the variable is not isolated, even though there is only one term on the left side. The 6 in front of the Y is our problem. In order to get rid of it, we are going to have to divide both

sides of the inequality by 6.

6Y< 366 6

6 divided by 6 is 1, so those 6’s on the left side cancel each other out. On the right side, 36 divided by 6 is 6. Look at

that – we solved the inequality!

Click here to continu

e

Y < 6

If you have a whole number in front of a variable, you will have to divide both sides of the inequality. If the number is a fraction, you will have to multiply both sides of the inequality by the inverse of the fraction.

+ 8

You are going to start by adding 8 to both sides of the inequality – but that’s pretty much old news now,

right?


- 8 + 8 = 0, so those eights on the left side of the inequality cancel

each other out. On the right side of the inequality, we have 8 + 8,

which equals 16.

Click here to continue

-4x – 8 > 8

+ 8-4x > 16

There is gonna be an extra step in this one…but you’ll see that when you get there…

This inequality looks just like the last one. I just do the same thing, right?

Like Terms are terms whose variables (and their exponents such as the 2 in x2) are the same.


- 4x > 16

x < -4

Just like we usually do, we have to get rid of that -4 in front of the x by

dividing both sides by -4, and the -4’s on the left side of the inequality cancel

each other out.


When you divide both sides of an inequality by a negative number, you have to turn the sign around. Here, >

becomes < .

- 4

- 4

Now, it’s time for that extra step, right?

Remember, when you divide both sides of an inequality by a negative number, you have to switch the sign.


Just like we usually do, we are going to get rid of the 4 on the left side of the inequality by subtracting 4 from both

sides of the inequality. Then, the 4 and the -4 on the left side cancel each

other out.


-7 minus 4 is -11, so we are now down to 1/3x = -11.

< -7

+ 4

1 x3

Finally, the last inequality!

- 4

- 4

1 x = -113

Remember, when you divide both sides of an inequality by a negative number, you have to switch the sign.


How do we get rid of that 1/3 in front of the x? We are going to have to

multiply both sides of the inequality by the reciprocal of the fraction – which is

3. Click here to continueWhat is 1/3 times 3? 1 of course! So

those cancel each other out, x is isolated, and all we have to do is

multiply -11 by 3, which is -33, and our inequality is solved!

x < -113

1(3)

(3)

x < -33

Ms. Umberger

Transition to Algebra

Don’t panic when you see an inequality you would be amazed how easy they are!!

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Jason Solves Inequalities