Solve for x, 5x - 3 is less than 12 "and" 4x plus 1 is greater than 25.
So let's just solve for X in each of these constraints and keep in mind
that any x has to satisfy both of them
because it's an "and" over here
so first we have this 5 x
minus 3 is less than 12
so if we want to isolate the x
we can get rid of this negative 3
here by adding 3 to both sides
so let's add 3 to both sides of this inequality.
The left-hand side, we're just left with a 5x, the minus 3 and the plus 3 cancel out.
5x is less than 12 plus 3 is 15.
Now we can divide both sides by positive 5,
that won't swap the inequality since 5 is positive.
So we divide both sides by positive 5
and we are left with just from this constraint
that x is less than 15 over 5, which is 3.
So that constraint over here.
But we have the second constraint as well.
We have this one, we have 4x plus 1
is greater than 25.
So very similarly we can substract one from both sides
to get rid of that one on the left-hand side.
And we get 4x, the ones cancel out.
is greater than 25 minus one is 24.
Divide both sides by positive 4
Don't have to do anything to the inequality since
it's a positive number.
And we get x is greater than
24 over 4 is 6.
And remember there was that "and" over here.
We have this "and".
So x has to be less than 3 "and" x has to be greater than 6.
So already your brain might be realizing
that this is a little bit strange.
This first constraint says that x needs to be less than 3
so this is 3 on the number line.
We're saying x has to be less than 3
so it has to be in this shaded area right over there.
This second constraint says that x has to be
greater than 6.
So if this is 6 over here, it says that x has to greater than 6.
It can't even include 6.
And since we have this "and" here.
The only x-es that are a solution for this compound inequality
are the ones that satisfy both.
The ones that are in the overlap
of their solution set.
But when you look at it right over here it's clear that
there is no overlap.
There is no x that is both greater than 6 "and" less than 3.
So in this situation we no solution.

聯立不等式 4 (英)

聯立不等式 4 (英) : 聯立不等式 4