~ 6.15 ~

Learning Targets

• I can graph the solutions to an inequality on a number line.

• I can solve inequalities by solving a related equation and then checking which values are solutions to the original inequality.

Here is an inequality: 3(10 - 2x) < 18. The solution to this inequality is all the values you could use in place of x to make the inequality true.

In order to solve this, we can first solve the related equation 3(10 - 2x) < 18 to get the solution x = 2. That means 2 is the boundary between values of x that make the inequality true and values that make the inequality false.

To solve the inequality, we can check numbers greater than 2 and less than 2 and see which ones make the inequality true.

Let’s check a number that is greater than 2: x = 5. Replacing x with 5 in the inequality, we get 3(10 - 2 • 5) < 18 or just 0 < 18. This is true, so x = 5 is a solution. This means that all values greater than 2 make the inequality true. We can write the solutions as x > 2 and also represent the solutions on a number line:

Notice that 2 itself is not a solution because it's the value of x that makes 3(10 - 2x) ​equal to 18, and so it does not make 3(10 - 2x) < 18 true.

For confirmation that we found the correct solution, we can also test a value that is less than 2. If we test x = 0, we get 3(10 - 2 • 0) < 18 or just 30 < 18. This is false, so x = 0 and all values of x that are less than 2 are not solutions.

Check Google Classroom!