# -2<5x-3<12 solve for xThe equation, as originally type in, had a -12 instead of just 12

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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: -2<5x-3<12 .

Solution:

Thereare two inequalities here: The first is -2 <5x-2. and the other inequality is 5x-3 <12.

First inequality:

-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:

5x-3>-2 (1)

5x-3<12 (2)

Let's solve the first inequality:

5x-3>-2

We'll add both sides the value 2. Because it's a positive value, the inequality remains unchanged.

5x-3+2>-2+2

5x-1>0

Let's add now the value 1, keeping unchanged the inequality:

5x>1

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:

5x-3<12

First, we'll move the the value -3, to the right side, by changing it's sign:

5x<12+3

5x<15

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).