Transcript 2, divide both sides by

Solving Multi-Step Inequalities
Section 2.4
Warm Up
Solve each equation.
1. 2x – 5 = –17
–6
2.
14
Solve each inequality and graph the solutions.
3. 5 < t + 9 t > –4
4.
a ≤ –8
Solve the inequality and graph the solutions.
45 + 2b > 61
45 + 2b > 61
–45
–45
2b > 16
b>8
0
2
4
6
Since 45 is added to 2b,
subtract 45 from both
sides to undo the
addition.
Since b is multiplied by 2,
divide both sides by 2
to undo the
multiplication.
8 10 12 14 16 18 20
Solve the inequality and graph the solutions.
8 – 3y ≥ 29
8 – 3y ≥ 29
–8
–8
Since 8 is added to –3y,
subtract 8 from both
sides to undo the
addition.
Since y is multiplied by –3,
divide both sides by –3
to undo the
multiplication.
Change ≥ to ≤.
–3y ≥ 21
y ≤ –7
–7
–10 –8 –6 –4 –2
0
2
4
6
8 10
Solve the inequality and graph the solutions.
–12 ≥ 3x + 6
–12 ≥ 3x + 6
–6
–6
Since 6 is added to 3x,
subtract 6 from both
sides to undo the
addition.
Since x is multiplied by 3,
divide both sides by 3
to undo the
multiplication.
–18 ≥ 3x
–6 ≥ x
–10 –8 –6 –4 –2
0
2
4
6
8 10
Solve the inequality and graph the solutions.
Since x is divided by –2,
multiply both sides by –2
to undo the division.
Change > to <.
x + 5 < –6
–5 –5
Since 5 is added to x,
subtract 5 from both
sides to undo the
addition.
x < –11
–11
–20
–16
–12
–8
–4
0
Solve the inequality and graph the solutions.
Since 1 – 2n is divided by 3,
multiply both sides by 3
to undo the division.
Since 1 is added to –2n,
subtract 1 from both sides
to undo the addition.
1 – 2n ≥ 21
–1
–1
–2n ≥ 20
Since n is multiplied by –2,
divide both sides by –2 to
undo the multiplication.
Change ≥ to ≤.
n ≤ –10
–10
–20
–16
–12
–8
–4
0
Solve the inequality and graph the
solutions.
Multiply both sides by 6,
the LCD of the
fractions.
4f + 3 > 2
–3 –3
4f
> –1
Distribute 6 on the left
side.
Since 3 is added to 4f,
subtract 3 from both
sides to undo the
addition.
Solve the inequality and graph the solutions.
3 + 2(x + 4) > 3
Distribute 2 on the left side.
3 + 2(x + 4) > 3
3 + 2x + 8 > 3
2x + 11 > 3
– 11 – 11
2x
Combine like terms.
Since 11 is added to 2x,
subtract 11 from both
sides to undo the
addition.
> –8
Since x is multiplied by 2,
divide both sides by 2 to
undo the multiplication.
x > –4
–10 –8 –6 –4 –2
0
2
4
6
8 10
Solve the inequality and graph the solutions.
Multiply both sides by 8, the LCD
of the fractions.
Distribute 8 on the right side.
5 < 3x – 2
+2
+2
7 < 3x
Since 2 is subtracted from 3x,
add 2 to both sides to undo
the subtraction.
Example 3
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 is 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
<
daily
cost at
We Got
Wheels
38
plus
+
$0.20
per mile
0.20
times
# of
miles.

m
55 < 38 + 0.20m
Since 38 is added to 0.20m, subtract
55 < 38 + 0.20m
38 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.
Example 4
The average of Jim’s two test scores must
be at least 90 to make an A in the class.
Jim got a 95 on his first test. What grades
can Jim get on his second test to make an
A in the class?
Let x represent the test score needed. The
average score is the sum of each score divided
by 2.
First
test
score
(95
plus
+
second
test
score
x)
divided
by

number
of scores
2
is greater
than or
equal to
≥
total
score
90
Since 95 + x is divided by 2, multiply
both sides by 2 to undo the division.
95 + x ≥ 180
–95
–95
Since 95 is added to x, subtract 95 from
both sides to undo the addition.
x ≥ 85
The score on the second test must be 85 or higher.