Transcript Solving Inequalities

Solving
Inequalities

Warm – Up!!
 Solve the following equations
1. 7 = x – 8
2. 2m + 3 = 31
3. 3x – 12 = 27
One Step Inequalities
An inequality says that two values are not equal and we can
represent/ show they are not equal in 4 different ways.
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Inequalities are similar to equations!
Solving One-Step Inequalities
 Treat the inequality symbol (<, >, ≤,≥) as an equal sign and
solve.
 If you multiply or divide by a negative number the inequality
symbol flips the opposite way.
 Examples:
1.) x – 7 > 10
2.) 2d < 21
Is It A Solution?
 You can determine if a given value is a solution to the
inequality by evaluating an expression.
 Example:
Are the following values solutions of x < 9
A.) 6
B.) -2
C.) 18
2
Solving Multi Step Inequalities
 When solving multi-step inequalities, treat the
inequalities (<, >, <, >) like equal signs
 Remember to flip the inequality when multiplying or
dividing by negative numbers
 Example: Simplify and graph the inequality
-2(m – 3) > 14
Practice
1.) Is 3 a solution to 2 - 4x > 14?
2.) Is -2 a solution to 10 > 9x - 4?
3.) 2k +4 < k + 8
4.) 2j – 10 – 9j > -3
More Practice
5.) b > 9
6.) j < 10 + 7
-2
7.) -7x > 14
8.) 6 + d > 3
Exit Ticket
 Solve the following inequalities:
1) y + 5 > 9
2) -8x < 64
3) Simplify the following inequality and graph it on a
number line:
10w – 7w + 8 > 20
Warm – Up!!
 Solve the following inequalities:
1) 2 - m > 12
2) -8k < 64
 Solve the following equations for c:
1) 10c – 3 = 13c
2) c + 1 = 4
2
Translating
 Write and solve the following equations:
7=x–8
2m + 3 = 31
 Write an equation modeling the following:
The sum of 9 and k is 18
Seven minus v is 3
23 less than x is 10
From English To Inequality
 Look for the key terms: less, more/greater, less than or equal
to, greater/more than or equal to, at least, at most
 Examples: Translate the following
1.) You have to be at least 48 inches to ride the rollercoaster.
________________
2. The speed limit is 65 miles per hour.
_____________
Practice
 A number plus seven is less than 12.
__________________________
 5 less than a number is 2.
_________
 The standard size, s, of adult shoes ranges from
size 3 to size 25.
 Employees must work at least 20 years in order to
receive full benefits. ___________________
Practice
Mrs. Smith wrote “Eight less than three
times a number is greater than 15” on
the board. If x represents the number,
which inequality is a correct translation
of this statement?
(A)
(B)
(C)
(D)
3x – 8 > 15
3x – 8 < 15
8 – 3x > 15
8 – 3x < 15
Practice
Students in a ninth grade class measured
their heights, h, in centimeters. The
height of the shortest student was 155
cm, and the height of the tallest student
was 190 cm, Which inequality
represents the range of heights?
(A)
(B)
(C)
(D)
155 < h < 190
155 < h < 190
154 < h < 190
154 < h < 190
Practice