1. Lesson 6.3 Solve Multi-Step Inequalities
Essential Question: How do you solve multi-step inequalities?

2. Before we start…
Six more than 5 times a number x is greater than or equal to 31.
Can you write and solve this inequality?

3. How do you solve multi-step inequalities?
Use distributive property and/or combine like terms.
Isolate the variable using inverse operations.
Just remember to reverse the inequality symbol when multiplying or dividing by a negative number.

11. What about the number of solutions of an inequality?
If an inequality is equivalent to an inequality that is true, then the solutions are all real numbers.
If an inequality is equivalent to an inequality that is false, then the inequality has no solution.

14. Write and solve the inequality
Write and solve the inequality. Twice the sum of 4 and x is less than -16.

15. Write and solve the inequality
Write and solve the inequality. The difference of 10𝑥 and 3𝑥 is less than or equal to the sum of 4𝑥 and 21.

16. Write and solve the inequality
Write and solve the inequality. The sum of 2𝑥 and 4𝑥 is greater than or equal to the sum of 3𝑥 and 36.

17. Car Wash A gas station charges $2. 09 per gallon of gas and $8
Car Wash A gas station charges $2.09 per gallon of gas and $8.00 for a car wash. The gas station charges $0.10 less per gallon of gasoline if a customer also gets a car wash. What are the possible amounts (in gallons) of gasoline that you can buy if you also get a car wash and can spend at most $20?

18. Weaving A weaver spends $420 on supplies to make wall hangings and plans to sell the wall hangings for $80 each. Write and solve an inequality that gives the possible numbers w of wall hangings the weaver needs to sell in order for the profit to be positive.

19. How do you solve multi-step inequalities?

20. Ticket Out the Door