Assignment 1: 04-Solving Inequalities
Assignment 2: 05-Solving Inequalities Practice
Assignment 3: Solving Inequalities Word Problems
Take a look at the expression below:
6x + 4 > 40
If you imagine that the greater than or equal to sign were just an equal sign, you could solve for x using the rules for solving an equation. Well, guess what… solving an inequality works the exact same way. To solve for x in the previous inequality you would want to subtract the 4 and divide by 6.
This solution tells us we could pick any number greater than or equal to 6 and it would make our expression true. For example 10 > 6. If you put that into the original expression, 6(10) + 4 = 60 + 4 = 64 and 64 > 40 is a true statement, so our solution is correct. the final step would be to graph it. The > tells us that we will use a closed circle on the 6. It also tells us our arrow is going to point to the right, so our graph of that inequality is below.
There is one big difference when dealing with inequalities as compared to equations. This difference comes when dealing with negative numbers. You still perform the opposite operations the exact same way, and all of the rules for the operations still apply. The sign does switch directions when multiplying or dividing by a negative number. Here’s an example:
The reason for the switch has to do with the whole multiplying two negatives makes a positive. If you want to check the answer, pick a number less than -4, say -7. Put -7 into the original expression. -3(-7) + 6 = 21 + 6 = 27, and 27 > 18 is a true statement, therefore our solution is correct. The final thing we have left to do is to graph the inequality. We will use an open circle because it is only less than, not equal to, and the arrow will point to the left for less than.
