9514 1404 393
Explanation:
<u>Part B</u>:
Draw an open circle at x=5. Shade that portion of the number line that exists to the right of the open circle. The solution set is the shaded portion of the number line.
__
<u>Part C</u>:
Any value from the shaded portion of the number line can be used to check the inequality is true. The value at the open circle, or any value to the left of it can be used to check that the inequality is false. For example, one might use values of -5, 5, and 10. Choosing values that are multiples of 5 can make the arithmetic easier.
<u>x = -5 (expect false)</u>
-2/5(-5) < -2
10 < -2 . . . . False
<u>x = 5 (expect false)</u>
-2/5(5) < -2
-2 < -2 . . . . False
<u>x = 10 (expect true)</u>
-2/5(10) < -2
-4 < -2 . . . . True
Solve:
We need to isolate k, so multiply both sides by the denominator, which is 64. When we do that, the fraction will cancel and we get:
If you want to check, plug in your answer to the original equation and see if it is true:
This statement is true, so .