Page 30 - Math Course 1 (Book 2)

Solving Open Sentence Equations

MO. 7 - L5b

Solve Open Sentence

Inequalities

Vocabulary A-Z
Let us learn some vocabulary OUTDOORS
A four-wheel-drive tour of
Canyon de Chelly National
Monument in Arizona costs
$45 for the f rst vehicle and
inequality
$15 for each additional
an open sentence that contains the symbol <, ≤, >, vehicle. How many vehicles
or ≥ is called an inequality. can the Velo family take on
the tour if they want to spend no more than $100?
y 18 – y < 10 True or False
The expression 45 + 15n can be used
8 18 – 8 ⩻ 10 → 10 ≮10 false to represent the cost of n + 1 vehicles.
Explore The family wants to spend no more than
$100. The situation can be represented
9 18 – 9 ⩻ 10 → 9 < 10 true by the inequality 45 + 15n ≤ 100.
Since no replacement set is given,
10 18 – 10 ⩻ 10 → 8 < 10 true Plan estimate to f nd reasonable values
for the replacement set.
11 18 – 11 ⩻ 10 → 7 < 10 true
Start by letting n = 6 and then adjust
Solve
values up or down as needed.
Let’s Begin 45 + 15n ≤ 100 Original inequality
45 + 15(6) ≤ 100 n = 6
45 + 90 ≤ 100 Multiply 15 and 6.
135 ≤ 100 Add 45 and 90.
Real World Example
The estimate is too high. Decrease the value of n.

FISHING n 45 + 15n ≤ 100 Reasonable
Carlos needs $35 or more for a f shing trip. He has
already bought a ticket for the charter boat for $13. 5 45 + 15(5) ⩻ 100 → 120 ≰ 100 too high
Does Carlos need to save $20, $21, $22, or $23 to
have enough money for the f shing trip? Find the 4 45 + 15(4) ⩻ 100 → 105 ≰ 100 almost
solution set for s + 13 > 35, if the replacement set
is {20, 21, 22, 23}.
3 45 + 15(3) ⩻ 100 → 90 ≤ 100 almost
Replace s in s + 13 > 35 with each value in the
replacement set. 2 45 + 15(2) ⩻ 100 → 75 ≤ 100 too high
a s + 13 ≥ 35 → 35 True or False
20 20 + 13 ≥ 35 → 33 ⩼ 35 false Check The solution set is {0, 1, 2, 3}. In
addition to the f rst vehicle, the Velo
21 21 + 13 ≥ 35 → 34 ⩼ 35 false family can take up to 3 additional
22 22 + 13 ≥ 35 → 35 ≥ 35 true vehicles and spend no more than $100.
23 23 + 13 ≥ 35 → 36 ≥ 35 true
They can take as many as
The solution set for s + 13 ≥ 35 Answer 3 + 1 or 4 vehicles and stay
Answer is {22, 23}. Carlos could save within their budget.
$22 or $23 for the f shing trip.

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