This week in precalc 11, I learnt how to graph and solve one-variable inequalities. I chose this subject because it serves as the foundation for understanding how to draw more complicated inequality graphs, such as those involving two variables.

In this first example, we don’t have to solve the inequality, but we have to graph it. The type of dot you use depends on the greater than or less than sign. If the greater than or less than sign has a line under it, you will use the solid dot as it indicates that x can also be the value, if the sign does not have a line, use a hollow dot as it indicates the value is not included. In this example we will use a solid dot. Place the solid dot on the value of x, 3. To determine where the arrow will point it depends if it is a greater than or less than sign in the inequality. When x is on the left side of the inequality, the sign pointing to the right like an arrow, is greater than, but if it is pointing towards x, left, it is less than. In this case the arrow will point to the left.

For this example, the first thing you want to do is solve the inequality, you do this by isolating the variable x. Something you have to remember when solving inequalities is that when you divide by a negative, you must flip the greater than or less than sign. This is because dividing by a negative makes the greater than or less than sign no longer true to the equation. After isolating the variable, you can then graph the inequality. Figure out the type of dot you will use as explained above and graph it. Next, determine where the arrow will point, in this case it will point to the right.

hope this helps:)