www.VirtualNerd.com

How Do You Find a Solution Set When You Have A Replacement Set?

Find the solution set for the following: x + 5 < 20 from the replacement set {5, 10, 15, 20}.

Summary

  1. The replacement set is the set you are given
  2. The solution set is the set you are looking for
  3. The inequality symbol < means "less than"
  4. The solution set will contain the elements from the replacement set that make x+5 less than 20
  5. 5 is in the solution set because 5+5 is less than 20
  6. 10 is in the solution set because 10+5 is less than 20

Notes

    1. We need to evaluate the expression x+5 for each value of the replacement set
    1. Replace the variable, x, with the first value, 5
    2. When x=5, our expression equals 10
    1. Replace the variable, x, with the second value, 10
    2. When x=10, our expression equals 15
    1. Replace the variable, x, with the third value, 15
    2. When x=15, our expression equals 20
    1. Replace the variable, x, with the fourth value, 20
    2. When x=20, our expression equals 25
    1. The expression we evaluated in the last step was the left side of our original inequality
    2. The inequality symbol < means "less than"
    3. In order to be true, our new values must be less than 20
    1. We need to put the new values that we found back into the original inequality
    2. If the value on the left hand side is less than 20, the statement is true
    1. The inequality symbol < means "less than"
    2. Ask: Is 10 less than 20?
    3. Our first new value, 10, is less than 20, so it gives us a true statement
    4. Ask: Is 15 less than 20?
    5. Our second new value, 15, is less than 20, so it gives us a true statement
    6. Ask: Is 20 less than 20?
    7. Our third new value, 20, is NOT less than 20, so it does NOT give us a true statement
    8. Ask: Is 25 less than 20?
    9. Our fourth new value, 25, is NOT less than 20, so it does NOT give us a true statement
    1. For each of our true statements, we need to go back and find out what value of x we used to make the statement true
    1. The x values that made the inequality true are the elements of our solution set
    2. The inequality symbol < means "less than"
    3. We got the true statement 10<20 when x=5
    4. So 5 is in our solution set
    5. We got the true statement 15<20 when x=10
    6. So 10 is in our solution set