What you need to do here is to treat this just as if it were an equation rather than an inequality. What that means is that you can solve for X just like if it were an equation.

So, what you need to do first is get rid of the 2 in the middle. You do that by subtracting it from all three sides. That gets you

-1<3x<10

So then you divide everything by 3 to solve for X.

That gives you

-.33<x<3.33

So we know that x is some number that is between -.33 and 3.33.

1 < 3x + 2 < 12

Basically we have to get the " x " alone first. So subtract two on all 3 sides

By subtracting, your equation should look like

**-1 < 3x < 10 **now divide all 3 sides by 3

By dividing all 3 sides by 3 your equation should be

**-1/3 < x < 10/3 also -.33 < x < 3.33** which is your answer

sorry i had a typo the second equation onward should look like this: -1<3X<10

and -1/3<X<10/3

1 < 3x + 2 < 12

Treat it just like an equation.

Isolate the variable by undoing the addition first:

1 - 2 < 3x + 2 - 2 < 12 - 2

-1 < 3x < 10

Undo the multiplication next

-1/3 < x < 10/3

1<3x+2

To solve the inequation above, we have to add the value

(-1) in order to cancel the free term, 1, from the left side.

1-1<3x+2-1

0<3x+1

We'll move the unknown term in the left side of the inequality:

-3x<1

We'll multiply the inequality with the value (-1), therefore the inequality will become opposite :

3x**>-1**

**x>-(1/3)**

**That means that the solution of the first inequation will be the interval (-1/3, infinity).**

3x+2<12

To solve the inequation above, we have to add the value

(-12) in order to cancel the free term, 12, from the right side.

3x+2-12<12-12

3x-10<0

We'll move the value (-10), with the opposite sign, to the right side:

3x<10

**x<10/3**

**The solution of the second inequality is the interval of values (- infinity, 10/3).**

**It's important to not miss the aspect of simultaneity of both inequations, so that the common solution of the double inequation is found by intersecting ranges of values:**

**(-1/3, infinity)intersected(- infinity,10/3)=(-1/3, 10/3)**