-2<5x-3<12 solve for xThe equation, as originally type in, had a -12 instead of just 12
I think that you have made some sort of mistake in typing in your equation. A number cannot be greater than -2 but, at the same time, smaller than -12. So I am assuming that the correct equation is
-2 < 5x - 3 < 12
If that is truly what the equation is, we must first add 3 to all sides of the equation. Now you have
1 < 5x < 15
Then divide all sides by 5 so that you will only have x in the middle. Now you have
.2 < x < 3
To solve the inequality, first add 3
-2+3 < 5x -3+3 < 12 +3
1 < 5x < 15
Now divide by x factor which is (5)
1/5 < 5x/5 < 15/5
1/5 < x < 3
Then x values belong to the interval (1/5,3)
To solve the inequality: -2<5x-3<12 .
Thereare two inequalities here: The first is -2 <5x-2. and the other inequality is 5x-3 <12.
-2 < 5x-3. The solution does not change if we add the equals to both sides. So We add 3 to both sides.
-2+3 < 5x-3+3. Simplifying<, we get:
-1 < 5x. We can multiply bot sides by equal psitive quantity without changing the iequlity or its solution.
-1/5 < 5x/5. Or
-1/5 < x..................(1)
Taking the other inequality 5x-3 < -12 and proceed by adding both sides, 3.So,
5x-3+3 <12. Or
5x < 12+3 = 15. Multiplying by (1/5) both sises, we get:
5x(1/5) =<15(1/5) Or
x < 3..............(2).
Thus from (1) and (2) we get: x < 3 Or x > -1/5. Or
x takes any value inside the interval (-1/5 , 3 )
In fact, we have to solve 2 inequalities simultaneously:
Let's solve the first inequality:
We'll add both sides the value 2. Because it's a positive value, the inequality remains unchanged.
Let's add now the value 1, keeping unchanged the inequality:
We'll divide by 5, both sides:
x>1/5 so x belongs to the interval (1/5 , +inf.)
Now, let's solve the second inequality:
First, we'll move the the value -3, to the right side, by changing it's sign:
Now, we'll divide by 5:
x<3, so x belongs to the interval (-inf. , 3).
The common solution is the intersection of both intervals and we'll get the interval (1/5 , 3).