Transcript alg lesson 1.4

1.4 Write Equations and Inequalities
Warm Up
Lesson Presentation
Lesson Quiz
1.4
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.
ANSWER
50 + 2t, where t is the number of tickets;
$68
1.4
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
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1.
Guided Practice
Write an equation or an inequality: The quotient of a
number p and 12 is at least 30.
ANSWER
p > 30
12 –
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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) – 5 ?= 6
7=6 X
3 is not a solution.
c. 2z + 5 > 12
2(3) + 5 ?> 12
11 > 12 X
3 is not a solution.
d. 5 + 3n ≤ 20
?
5 + 3(3) ≤ 20
14 ≤ 20
3 is a solution.
1.4
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 + 3 >
– 21; 9
solution
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Example 3
Equation
Think
x + 4 = 10
What number
plus 4 equals 10?
6
6 + 4 = 10
b. 20 – 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
d.
a =9
5
a.
Solution
What number
45
divided by 5 equals 9?
Check
45
5 =9
1.4
Guided Practice
Solve the equation using mental math.
5. m + 6 = 11
5
6. 5x = 40
8
7. r = 10
4
40
1.4
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?
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Example 4
SOLUTION
STEP 1
Write a verbal model. Let p be the regular price of 4
tickets. Write an equation.
p
10
=
17
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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
Find the cost per person:
ANSWER
Each person pays $6.75.
$27
= $6.75 per person.
4 people
1.4
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.
1.4
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
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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.
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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
1.4
Lesson Quiz
Write an equation or an inequality.
1.
3 less than twice a number n is 12.
ANSWER
2.
The product of 5 and a number k is no more than 30.
ANSWER
3.
2n – 3 = 12
5k <
– 30
Check whether 2 is a solution of the inequality
3p + 2 > 8
ANSWER
8 >/ 8; 2 is not a solution.
1.4
4.
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.
ANSWER
Yes; the inequality h + 8.5 >
– 25
represents the situation. If you
substitute 16.5 for h, 16.5 + 8.5 = 25
and 25 >
– 25.