Question

Solve the inequality. Write the solution in​ set-builder notation.


-3(8x + 3) > - 9 - 24x

Answer 1

Starting with the given inequality:

-3(8x + 3) > -9 - 24x

Let's first distribute the -3 on the left side of the inequality:

-24x - 9 > -9 - 24x

Now let's simplify by subtracting -24x from both sides:

-24x - 24x - 9 > -9 - 24x - 24x

-48x - 9 > -9 - 48x

Next, let's simplify by adding 48x to both sides:

-48x + 48x - 9 > -9 - 48x + 48x

-9 > -9

This is a contradiction. The inequality -9 > -9 is not true for any value of x. Therefore, there is no solution to the inequality.

The solution in set-builder notation is an empty set:

{}