1. Write Equations and Inequalities
Warm Up
Lesson Presentation
Lesson Quiz

2. Warm-Up
1. Write an expression for the phrase: 4 times the
difference of 6 and a number y.
ANSWER
4(6 – y)
2. A museum charges $50 for an annual membership
and then a reduced price of $2 per ticket. Write an
expression to represent the situation. Then find the
total cost to join the museum and buy 9 tickets.
50 + 2t, where t is the number of tickets;
$68
ANSWER

3. Example 1
Verbal Sentence
Equation or Inequality
a. The difference of twice a
number k and 8 is 12.
2k – 8 = 12
b. The product of 6 and a number n is at least 24.
6n ≥ 24
c. A number y is no less than 5 and no more than 13.
5 ≤ y ≤ 13

4. Guided Practice
1. Write an equation or an inequality: The quotient of a number p and 12 is at least 30.
ANSWER p 12
> – 30

5. Example 2
Check whether 3 is a solution of the equation or inequality.
Equation/Inequality
Substitute
Conclusion
a. 8 – 2x = 2
8 – 2(3) 2 ? =
2 = 2 3 is a solution.
b. 4x – 5 = 6
4(3) – ? =
7 = 6 3 is not a solution. X
c. 2z + 5 > 12
2(3)
> ?
11 > is not a solution. X
d n ≤ 20
5 + 3(3) ≤ ?
14 ≤ is a solution.

6. Guided Practice
Check whether the given number is a solution of the equation or inequality.
2. 9 – x = 4; 5
solution
3. b + 5 < 15; 7
solution
4. 2n ; 9
> –
solution

7. Example 3
Equation
Think
Solution
Check
a. x + 4 = 10
What number plus 4 equals 10? 6
6 + 4 = 10
b – y = 8
20 minus what number equals 8? 12
20 –12 = 8
c. 6n = 42
6 times what number equals 42? 7
6(7) = 42 a 5 = 9 d. 45 5 = 9
What number divided by 5 equals 9? 45

8. Guided Practice
Solve the equation using mental math.
5. m + 6 = 11 5
6. 5x = 40 8
7. r = 10 4 40

9. Example 4
Mountain Biking
The last time you and 3 friends went to a mountain bike park, you had a coupon for $10 off and paid $17 for 4 tickets. What is the regular price of 4 tickets? If you pay the regular price this time and share it equally, how much does each person pay?

10. Example 4
SOLUTION
STEP 1
Write a verbal model. Let p be the regular price of 4 tickets. Write an equation. p 10 = 17 

11. Example 4
STEP 2
Use mental math to solve the equation p – 10 = 17. Think: 10 less than what number is 17? Because 27 – 10 = 17, the solution is 27.
ANSWER
The regular price for 4 tickets is $27.
STEP 3
$27
4 people
Find the cost per person:
= $6.75 per person.
ANSWER
Each person pays $6.75.

12. Guided Practice
WHAT IF? In Example 4, suppose that the price of 4 tickets with a half-off coupon is $15. What is each person’s share if you pay full price?
ANSWER
Each person pays $7.50.

13. Example 5
Basketball
A basketball player scored 351 points last year. If the player plays 18 games this year, will an average of 20 points per game be enough to beat last year’s total?
STEP 1
SOLUTION
Write a verbal model. Let p be the average number of points per game. Write an inequality. 18  p
>
351

14. Example 5
STEP 2
Check that 20 is a solution of the inequality 18p > 351. Because 18(20) = 360 and 360 > 351, 20 is a solution.
ANSWER
An average of 20 points per game will be enough.

15. Guided Practice
WHAT IF? In Example 5, suppose that the player plays 16 games. Would an average of 22 points per game be enough to beat last year’s total?
ANSWER
Yes

16. Lesson Quiz
Write an equation or an inequality.
less than twice a number n is 12.
ANSWER
2n – 3 = 12
2. The product of 5 and a number k is no more than 30.
ANSWER 5k
< – 3.
Check whether 2 is a solution of the inequality
3p + 2 > 8
ANSWER
; 2 is not a solution. /
>

17. Lesson Quiz
You need to practice a gymnastic routine for at least 25 hours. You have already practiced 8.5 hours. If you practice for another 16.5 hours, will you reach your goal? Explain. 4.
ANSWER
Yes; the inequality h
represents the situation. If you substitute 16.5 for h, = 25
and
> –