Framing and Solving Inequalities
Presentation
•
Mathematics
•
10th Grade
•
Hard
James Gonzalez
FREE Resource
16 Slides • 10 Questions
1
Solving Inequalities
2
Multiple Choice
Evaluate the expression |4w + 3| if w = –2.
5
7
11
12
3
Multiple Choice
Evaluate the expression |2x + y| if x = 1.5 and y = 4.
5
7
10
20
4
Multiple Choice
Evaluate the expression 5|xy – w|
if w = –2, x = 1.5, and y = 4.
5
10
20
40
5
Multiple Choice
Solve the equation |b + 20| = 21.
{–41, 1}
{–41, –1}
{–1, 1}
{1, 2}
6
Multiple Choice
Solve the equation –4|a + 5| = –8.
{7, 3}
{2, 3}
{-7, -3}
{-2, 3}
7
Multiple Choice
What is the solution to the equation
2|3x – 1| – 1 = –5?
x = −31
x = 1
x = −31 and x = 1
no solution
8
You solved equations involving absolute
values. (Lesson 1–4)
• Solve one-step inequalities.
• Solve multi-step inequalities.
9
• set-builder notation
10
11
Solve an Inequality Using Addition or Subtraction
Solve 4y – 3 < 5y + 2. Graph the solution set on a number line.
12
Answer: Any real number greater than –5 is a solution
of this inequality.
A circle means that this
point is not included in
the solution set.
Solve an Inequality Using Addition or Subtraction
13
Multiple Choice
Which graph represents the solution to
6x – 2 < 5x + 7?
14
15
Solve an Inequality Using Multiplication or Division
16
Solve an Inequality Using Multiplication
or Division
A dot means that this
point is included in the
solution set.
17
Multiple Choice
What is the solution to –3x ≥ 21?
{x | x ≥ –7}
{x | x ≤ –7}
{x | x ≤ 7}
{x | x ≥ 7}
18
Solve an Inequality Using Multiplication or Division
19
Solve Multi-Step Inequalities
20
Multiple Choice
What is the solution to −2x > 3x + 5 ?
21
Write and Solve an Inequality
CONSUMER COSTS Javier has at most $15.00 to spend today. He buys a bag of pretzels and a bottle of juice for $1.59. If gasoline at this store costs $2.89 per gallon, how many gallons of gasoline, to the nearest tenth of a gallon, can Javier buy for his car?
Understand
Let g = the number of gallons of gasoline that Javier buys. The total cost of the gasoline is 2.89g. The cost of the pretzels and juice plus the total cost of the gasoline must be less than or equal to $15.00.
22
Write and Solve an Inequality
Original inequality
Subtract 1.59 from
each side.
Simplify.
The cost of
pretzels & juice
plus
the cost
of gasoline
is less than
or equal to
$15.00.
1.59
+
2.89g
15.00
Plan
Write an inequality.
Solve
23
Write and Solve an Inequality
Divide each side
by 2.89.
Simplify.
Answer: Javier can buy up to 4.6 gallons of gasoline
for his car.
Check
Since
is actually greater than 4.6,
Javier will have enough money if he gets no
more than 4.6 gallons of gasoline.
24
A. A
B. B
C. C
D. D
A
B
C
D
0%
0%
0%
0%
A. up to 700 miles
B. up to 800 miles
C. more than 700 miles
D. more than 800 miles
25
Multiple Choice
Jeb wants to rent a car for his vacation. Value Cars rents cars for $25 per day plus $0.25 per mile. How far can he drive for one day if he wants to spend no more that $200 on car rental?
up to 700 miles
up to 800 miles
more than 700 miles
more than 800 miles
26
Questions?
Solving Inequalities
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