choose the correct solution and graph for the inequality
-y/2<3
To find the correct solution to the inequality, we first need to solve for y. Our inequality is:
-\( \frac{y}{2} \) < 3
To solve for y we should perform the following steps:
1. Multiply both sides by -2 to get rid of the fraction (and remember that multiplying or dividing by a negative number will flip the direction of the inequality):
y > -6 (the inequality sign flips because we multiplied by -2, which is negative)
So the solution to the inequality -\( \frac{y}{2} \) < 3 is y > -6.
Let's graph this on a number line:
---------(-6)--------->
On a number line:
- The open circle at -6 represents that -6 is not included in the solution (because the inequality is strictly greater than, not greater than or equal to).
- The arrow going to the right indicates all the numbers greater than -6 are included in the solution.
The inequality y > -6 includes all real numbers that are greater than -6.