Question

Help meee please

Graph the inequality and give interval notation for the solution. Use two o's (as in octopus) for infinity and a U for union as needed.

-9x+1>19 or -8x+4<=-12

Answer 1

To graph the inequality and find the interval notation for the solution, we'll start by solving each inequality separately and then finding the intersection of their solution sets.

First, let's solve the first inequality:

-9x + 1 > 19

-9x > 18

x < -2

The solution set for this inequality is all x-values less than -2. We can graph this on the number line as an open dot at -2, indicating that -2 is not part of the solution.

Next, let's solve the second inequality:

-8x + 4 <= -12

-8x <= -16

x >= 2

The solution set for this inequality is all x-values greater than or equal to 2. We can graph this on the number line as a closed dot at 2, indicating that 2 is part of the solution.

Now, we'll find the intersection of the solution sets. The solution to the system of inequalities is the set of all x-values that satisfy both inequalities. In this case, the solution is the interval (2, oo).

The interval notation for the solution is (2, oo), which means that all x-values greater than or equal to 2 and less than infinity satisfy the system of inequalities.