
Did you get the closed interval from negative 1 to 1? If so, you should be very

proud of yourself. I know I am. Let's see how we got that solution. Remember

when you're working with a compound inequality that's written in this form, we

can perform operations as long as we do the same operation, to all three

portions of the quation. The first thing I want to do is to get rid of this

fraction by multiplying through by the least common denominator, and the least

common denominator is 2. When I multiply 2 by negative 3, I get negative 6. When

I multiply 2 by 5 x minus 1 over 2, I'm simply left with 5 x minus 1, and when I

multiply 2 times 2, I get 4. Next I'm going to add 1 to each part of the

equation so I can isolate the variable in the middle. When I do that, negative 6

plus 1 is negative 5, and 4 plus 1 is positive 5. Now I can divide through by 5.

Negative 5 divided by 5 is negative 1, less than or equal to x, less than or

equal to 5 over 5 is positive 1. Let's draw that on the number line. This

portion of the inequality says that negative 1 is less than or equal to x, which

is the same as x is greater than or equal to negative 1. So, that means we're

going to be going in that direction.

This portion of the equation says x is less than or equal to positive 1, so we

use a square bracket and the answer's going here. So we have the interval from

negative 1 to 1 using the square brackets.