You can
put this solution on YOUR website!In equation form you are given:
.
.
You can pretty much work these using the same procedures that you would to solve an equation.
.
However, there is an exception. This exception is that in solving for x if you ever have to
MULTIPLY or DIVIDE both sides by a NEGATIVE quantity, then you also have to reverse the
direction of the inequality sign.
.
Let's work this problem.
.
If this were an equation, you would solve for x by dividing both sides by 24 because 24
is the multiplier of x. So let's divide both sides by +24 to get:
.
.
Notice that on the left side if you divide both the numerator and denominator by 12 you are
left with
and on the right side the 24 in the numerator cancels with the 24
in the denominator. Therefore, all you are left with is:
.
.
That's the answer. Now, what does it mean? It says that
is greater than or equal
to x. (Remember that the inequality sign always points to the smaller quantity.)
.
This also means the same as x is less than or equal to
. For the purposes of
graphing this answer, you can draw a number line. Then put a dot at the point
.
x can have that value. x can also be less than that number. That means that x can be any
value to the left of the point at
. So you make the number line to the left of the
point
a very heavy line to indicate that x can be on that part of the line.
.
Hopefully this makes some sense to you. In solving this problem we didn't have to multiply
or divide both sides by a negative number, so we didn't need to use the rule about
changing the direction of the inequality sign. It just stayed the same direction
throughout all our work.
.
Remember the goal is to solve inequalities for +x. If you have a problem that you can solve
for -x, then do so. But at the very end of the problem you will need to multiply the -x by
-1 to change it to +x. And when you multiply one side by -1 you must also multiply the
other side by -1 ... and that means that you also need to reverse the direction of the
inequality sign because you multiplied both sides by a minus number.
You can
put this solution on YOUR website!
Flip the sides so the variable is on the left side
Divide both sides by 24 to isolate x
Reduce
So our answer is
or
in decimal form
Start with the given inequality:
Now lets graph
Start with the given inequality:
Now let's graph
Set up a number line:
Now plot the point x=-0.5 on the number line
Now pick any test point you want, I'm going to choose x=0, and test the inequality
Plug in
Since this inequality is
not true, we simply shade the entire portion that does
not contain the point x=0 using the point x=-0.5 as the boundary. This means we shade everything to the left of the point x=-0.5 like this:
Graph of
with the shaded region in blue
note: at the point x=-0.5, there is an
closed circle. This means the point x=-0.5 is included from the solution set.
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