-3 < 4 (2x-1)<12

Question

Solve each inequality. Write your answers in interval notation.

Answer 1

First distribute the 4 in the middle part. Your result is -3<8x-4<12

Next, add 4 to everything except for the variable. Your result is 1<8x<16

Finally, divide everything by 8. Your result is 1/8<x<2.

Read this as "x is greater than 1/8 but also less than 2" therefore in interval notation it would be (1/8,2) because x is basically stuck in between those two numbers and since there is no "or equal to" symbol, you cannot have any brackets.

Answer 2

Basically this will be solved like an equation, in that whatever we do to one side, we have to do to all the sides.

 

-3 < 4(2x - 1) < 12 

-3/4< 2x -1 < 3    <-- Divide everything by 4

1/4 < 2x < 4        <-- Add 1 to everything

1/8 < x < 2          <--Divide everything by 2

 

 

J.T.