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To solve
linear inequalities we will use
many of the same strategies we use when solving
linear equations.
First let's look at some examples of
linear inequalities:
x - 4 > 5
7x + 12 < 5x - 10
6y +9 ≥ 3y + 4
2a - 6 ≤ 5a -8
These look a lot like the equations you have already learned how to
solve don't they?
Look carefully......do you see what's different?
That's right! Instead of the 2 sides being connected by an
equal sign...they are connected
by an
inequality sign!
< (less than), >
(greater than), ≤ (less than or equal
to), and ≥ (greater than or equal to)
are the
4 inequality signs
we
will be using in this lesson.
Ok...now that we know what we're talking about,
let's look at an
example:
4x + 6 > 2x - 8
(Read as: 4 times a number
increased by 6 is greater than 2 times the number decreased by 8)
As stated earlier,
we follow many of the same strategies as we use when solving an
equation...
4x + 6 > 2x - 8
Step 1: (add-6) to both sides:
-6
- 6
4x > 2x - 14
Step 2: (add-2x) to both sides:
-2x -2x
2x > -14
Step3: divide both sides by 2:
2
2
x > 7 (answer)
Let's look
at another one....
This one is going to have a little trick
in it...
so read carefully!
5y - 8 ≤ 9y + 16
Step 1: add (+8) to both
sides:
+ 8
+ 8
5y ≤ 9y + 24
Step 2: add (-9y) to both
sides: -9y
-9y
Step 3:
-4y ≤ 24
Here
comes the trick! (÷
by -4)
-4
-4
When you divide in an inequality
y
≥ -6
(answer)
by a negative number
the order of
inequality sign is reversed!
Let's look
at one final example:
9x+10-4x-7 > 2(-2x+3)+11x-19
Step 1: Simplify:
5x + 3 > -4x + 6 + 11x -
19
Step 2: Simplify:
5x + 3 > 7x - 13
Step 3: add -3:
- 3 - 3
5x > 7x - 16
Step 4: add -7x:
-7x
-7x
-2x > -16
Step
5: divide by -2
-2 -2
x > 8 (answer)
Think
you're getting the idea?
For more practice
Click Here
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