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
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.
Click here for answer
< 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.
Click here for answer
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?
Click here for answer
- 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.
Click here to continue
- 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.
Click here to continue
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.
Click here to continue
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.
Click here to continue
-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.
Click here to continue
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!!
CLASS INFORMATION
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