Transcript Holt Algebra 1 3-2 - Austin Middle School

Solving Inequalities by
Inequalities word problems
3-2 Adding
or Subtracting
Warm Up
Lesson Presentation
Holt Algebra 1
Solving Inequalities by
3-2 Adding or Subtracting
Warm Up
1. –5a = 30
3.
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Solve each equation.
2.
–6
4.
–10
Solving Inequalities by
3-2 Adding or Subtracting
Example 1: Problem-Solving Application
Sami has a gift card. She has already
used $14 of the of the total value, which
was $30. Write and solve an inequality to
show how much more she can spend.
1
Understand the problem
The answer will be an inequality and a graph
that show all the possible amounts of money
that Sami can spend.
List important information:
• Sami can spend up to, or at most $30.
• Sami has already spent $14.
Holt Algebra 1
Solving Inequalities by
3-2 Adding or Subtracting
Example 1 Continued
2
Make a Plan
Write an inequality.
Let g represent the remaining amount of
money Sami can spend.
Amount
remaining
g
plus
amount
used
+
14
g + 14 ≤ 30
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is at
most
≤
$30.
30
Solving Inequalities by
3-2 Adding or Subtracting
Example 1 Continued
3
Solve
g + 14 ≤ 30
– 14 – 14
g + 0 ≤ 16
g ≤ 16
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Since 14 is added to g, subtract
14 from both sides to undo the
addition.
Solving Inequalities by
3-2 Adding or Subtracting
Example 1 Continued
4
Look Back
Check
Check the endpoint, 16.
g + 14 = 30
16 + 14 30
30 30 
Check a number less
than 16.
g + 14 ≤ 30
6 + 14 ≤ 30
20 ≤ 30
Sami can spend from $0 to $16.
Holt Algebra 1
Solving Inequalities by
3-2 Adding or Subtracting
Example 2
The Recommended Daily Allowance (RDA)
of iron for a female in Sarah’s age group
(14-18 years) is 15 mg per day. Sarah has
consumed 11 mg of iron today. Write and
solve an inequality to show how many more
milligrams of iron Sarah can consume
without exceeding RDA.
Holt Algebra 1
Solving Inequalities by
3-2 Adding or Subtracting
Example 2 Continued
1
Understand the problem
The answer will be an inequality and a graph
that show all the possible amounts of iron that
Sami can consume to reach the RDA.
List important information:
• The RDA of iron for Sarah is 15 mg.
• So far today she has consumed 11 mg.
Holt Algebra 1
Solving Inequalities by
3-2 Adding or Subtracting
Example 2 Continued
2
Make a Plan
Write an inequality.
Let x represent the amount of iron Sarah
needs to consume.
Amount
taken
11
plus
+
11 + x  15
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amount
needed
x
is at
most
15 mg

15
Solving Inequalities by
3-2 Adding or Subtracting
Example 2 Continued
3
Solve
11 + x  15
–11
–11
x4
0
1
2
3
4
5
6
7 8
9 10
Since 11 is added to x,
subtract 11 from both
sides to undo the addition.
Draw a solid circle at 4.
Shade all numbers less
than 4.
x  4. Sarah can consume 4 mg or less of iron
without exceeding the RDA.
Holt Algebra 1
Solving Inequalities by
3-2 Adding or Subtracting
Example 2 Continued
4
Look Back
Check
Check the endpoint, 4.
Check a number less
than 4.
11 + x = 15
11 + 4 15
15 15 
11 + 3  15
11 + 3  15
14  15 
Sarah can consume 4 mg or less of iron
without exceeding the RDA.
Holt Algebra 1
Solving Inequalities by
3-2 Adding or Subtracting
Example 3
Mrs. Lawrence wants to buy an antique bracelet
at an auction. She is willing to bid no more than
$550. So far, the highest bid is $475. Write and
solve an inequality to determine the amount
Mrs. Lawrence can add to the bid. Check your
answer.
Let x represent the amount Mrs. Lawrence can add to
the bid.
$475
plus
amount
can add
is at
most
$550.
475
+
x
≤
550
475 + x ≤ 550
Holt Algebra 1
Solving Inequalities by
3-2 Adding or Subtracting
Example 3 Continued
475 + x ≤ 550
–475
– 475
0 + x ≤ 75
x ≤ 75
Since 475 is added to x, subtract
475 from both sides to undo the
addition.
Check the endpoint, 75. Check a number less than 75.
475 + x ≤ 550
475 + x = 550
475 + 75 550
475 + 50 ≤ 550
525 ≤ 550
550 550
Mrs. Lawrence is willing to add $75 or less to the bid.
Holt Algebra 1
Solving Inequalities by
3-2 Adding or Subtracting
Example 4
Jill has a $20 gift card to an art supply store where 4
oz tubes of paint are $4.30 each after tax. What are
the possible numbers of tubes that Jill can buy?
Let p represent the number of tubes of paint that Jill
can buy.
$4.30
times
4.30
•
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number of tubes
is at most
$20.00.
p
≤
20.00
Solving Inequalities by
3-2 Adding or Subtracting
Example 4 Continued
4.30p ≤ 20.00
Since p is multiplied by 4.30,
divide both sides by 4.30. The
symbol does not change.
p ≤ 4.65…
Since Jill can buy only whole numbers of tubes,
she can buy 0, 1, 2, 3, or 4 tubes of paint.
Holt Algebra 1
Solving Inequalities by
3-2 Adding or Subtracting
Example 5
A pitcher holds 128 ounces of juice. What are the
possible numbers of 10-ounce servings that one
pitcher can fill?
Let x represent the number of servings of juice the
pitcher can contain.
10 oz
10
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times
number of
servings
is at most
128 oz
•
x
≤
128
Solving Inequalities by
3-2 Adding or Subtracting
Example 5 Continued
10x ≤ 128
Since x is multiplied by 10, divide both
sides by 10.
The symbol does not change.
x ≤ 12.8
The pitcher can fill 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,
10, 11, or 12 servings.
Holt Algebra 1
Solving Inequalities by
3-2 Adding or Subtracting
Example 6
To rent a certain vehicle, Rent-A-Ride charges $55.00
per day with unlimited miles. The cost of renting a
similar vehicle at We Got Wheels is $38.00 per day plus
$0.20 per mile. For what number of miles in the cost at
Rent-A-Ride less than the cost at We Got Wheels?
Let m represent the number of miles. The cost for
Rent-A-Ride should be less than that of We Got
Wheels.
Cost at
Rent-ARide
must be
less
than
55
<
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daily
cost at
We Got
Wheels
38
plus
+
$0.20
per mile
0.20
times
# of
miles.

m
Solving Inequalities by
3-2 Adding or Subtracting
Example 6 Continued
55 < 38 + 0.20m
Since 38 is added to 0.20m, subtract 8
55 < 38 + 0.20m from both sides to undo the addition.
–38 –38
17 < 0.20m
Since m is multiplied by 0.20, divide
both sides by 0.20 to undo the
multiplication.
85 < m
Rent-A-Ride costs less when the number of miles is
more than 85.
Holt Algebra 1