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Solving Inequalities
Do Now
Solve the equation:
x + 5 = 23
Graph the inequality:
x < 18
In order to solve an inequality…
x + 5 < 23
Solve it the same way as you would an
equation, but REMEMBER TO KEEP THE
INEQUALITY SYMBOL!
Let’s try some together. Solve each
inequality and show a check.
2) x + 13 ≥ 381) h/4 < 6
Now you try... Solve each inequality
and show a check.
4) 216 > 4x3) x – 45 ≤ 131
Solve each inequality and show a
check.
6) x/7 ≥ 95) 72 + x < 100
Circle the numbers that are solutions of
3k < 21
a) 4 b) 7 c) 12 d) 6
Write an inequality for the situation
below. Then solve the inequality.
You have $27 and want to invite the most
friends possible to go to a concert. What is
the greatest number of people, including
yourself who can go if each ticket is $4?
Do Now
1) A city law says that fences can have a maximum of 6 feet.
Write and graph the inequality.
2) a) Solve: 3x > 18
b) What are some possible solutions for the inequality?
Write an inequality for the situation below.
Then solve the inequality and write a
response.
The balance in your bank account is $290. You
write a check for $59. You want to keep your
balance above $150. Can you write another
check for $60? Justify your answer with a
written response.
Write, solve, and graph the inequality
for the situation below.
Kasey has been mowing lawns to save up money
for a concert. He earns $15 per hour and
needs at least $90 for his ticket. What is the
least amount of hours he needs to mow
lawns?
Write, solve, and graph the inequality
for the situation below.
Nancy has $250 in her bank account. She is
going to babysit to earn enough money to
reach her goal of having more than $600 in
her bank account.
Write, solve, and graph the inequality
for the situation below.
Ranger saves $70 each week. He needs to save
at least $2,800 to go to Europe. What is the
least amount of weeks he needs to save for?
Write, solve, and graph the inequality
for the situation below.
Heather has been saving money to go to a Twenty-One
Pilots concert. Her ticket will cost her $127. Her
bank insists that she keeps more than $400 in her
account to avoid being charged a fee. What is the
minimum amount of money that she must save, and
have in her account, in order to go to the concert
without having to pay a bank fee?
Write, solve, and graph the inequality
for the situation below.
Jenny wants to have a surprise party for her
mom. The restaurant can hold up to 200
people. If each table can seat no more than
10 people, what is the greatest amount of
tables that they would need?
Write, solve, and graph the inequality
for the situation below.
Nemo fish cost $3 each. You can spend at most
$27. Let f be the number of fish you can buy.
Group 1: The balance in your bank account is $590.
You write a check for $164. You want to keep your
balance above $175. Can you write another check for
$255? Graph your inequality and justify your answer
with a written response.
7h ≤ 77
h = 11
Group 2: James solved the inequality below. Analyze
his work to determine if he is correct or incorrect.
Justify your answer by showing work and explaining
your thoughts. Then graph the inequality.
7 7
Group 3: Solve, show a check, and
graph the inequality.
c/5 ≥ 36 What are two possible
solutions for x?
What value could not be a
possible solution for x?
Group 4: Solve the inequality and
show a check.
3b > 36 What are two possible
solutions for x?
What value could not be a
possible solution for x?
Group 5: Solve the inequality and
show a check.
x – 68 ≤ 123 What are two possible
solutions for x?
What value could not be a
possible solution for x?

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Solving inequalities

  • 2. Do Now Solve the equation: x + 5 = 23 Graph the inequality: x < 18
  • 3. In order to solve an inequality… x + 5 < 23 Solve it the same way as you would an equation, but REMEMBER TO KEEP THE INEQUALITY SYMBOL!
  • 4. Let’s try some together. Solve each inequality and show a check. 2) x + 13 ≥ 381) h/4 < 6
  • 5. Now you try... Solve each inequality and show a check. 4) 216 > 4x3) x – 45 ≤ 131
  • 6. Solve each inequality and show a check. 6) x/7 ≥ 95) 72 + x < 100
  • 7. Circle the numbers that are solutions of 3k < 21 a) 4 b) 7 c) 12 d) 6
  • 8. Write an inequality for the situation below. Then solve the inequality. You have $27 and want to invite the most friends possible to go to a concert. What is the greatest number of people, including yourself who can go if each ticket is $4?
  • 9. Do Now 1) A city law says that fences can have a maximum of 6 feet. Write and graph the inequality. 2) a) Solve: 3x > 18 b) What are some possible solutions for the inequality?
  • 10. Write an inequality for the situation below. Then solve the inequality and write a response. The balance in your bank account is $290. You write a check for $59. You want to keep your balance above $150. Can you write another check for $60? Justify your answer with a written response.
  • 11. Write, solve, and graph the inequality for the situation below. Kasey has been mowing lawns to save up money for a concert. He earns $15 per hour and needs at least $90 for his ticket. What is the least amount of hours he needs to mow lawns?
  • 12. Write, solve, and graph the inequality for the situation below. Nancy has $250 in her bank account. She is going to babysit to earn enough money to reach her goal of having more than $600 in her bank account.
  • 13. Write, solve, and graph the inequality for the situation below. Ranger saves $70 each week. He needs to save at least $2,800 to go to Europe. What is the least amount of weeks he needs to save for?
  • 14. Write, solve, and graph the inequality for the situation below. Heather has been saving money to go to a Twenty-One Pilots concert. Her ticket will cost her $127. Her bank insists that she keeps more than $400 in her account to avoid being charged a fee. What is the minimum amount of money that she must save, and have in her account, in order to go to the concert without having to pay a bank fee?
  • 15. Write, solve, and graph the inequality for the situation below. Jenny wants to have a surprise party for her mom. The restaurant can hold up to 200 people. If each table can seat no more than 10 people, what is the greatest amount of tables that they would need?
  • 16. Write, solve, and graph the inequality for the situation below. Nemo fish cost $3 each. You can spend at most $27. Let f be the number of fish you can buy.
  • 17. Group 1: The balance in your bank account is $590. You write a check for $164. You want to keep your balance above $175. Can you write another check for $255? Graph your inequality and justify your answer with a written response.
  • 18. 7h ≤ 77 h = 11 Group 2: James solved the inequality below. Analyze his work to determine if he is correct or incorrect. Justify your answer by showing work and explaining your thoughts. Then graph the inequality. 7 7
  • 19. Group 3: Solve, show a check, and graph the inequality. c/5 ≥ 36 What are two possible solutions for x? What value could not be a possible solution for x?
  • 20. Group 4: Solve the inequality and show a check. 3b > 36 What are two possible solutions for x? What value could not be a possible solution for x?
  • 21. Group 5: Solve the inequality and show a check. x – 68 ≤ 123 What are two possible solutions for x? What value could not be a possible solution for x?