Download 2.4 Day 2 and 2.5 - Algebra 1: Oak Park School District

Turn in 2.4 HW into Basket…Warm Up
2.4 Day 2 and 2.5
O C O T B E R 2 2 ND, 2 0 1 5
NAUMANN-BURKETT-SERVIO
Announcments
Learning Objectives
 Be able to write and solve inequalities (regular, and
compound) to answer questions from a problem
situation, and represent solutions on a number line
 Be able to evaluate and graph linear absolute value
equations, and inequalities
Some Extra 2.4 Examples
1) Solve, and graph the solution
-3(x+2) ≤ -12
X+2 ≥ 4
-2
 Step 1: Divide both
sides by -3. FLIP
THE SIGN.
 Step 2: Subtract 2
-2
x≥2
-2
-1
0
1
2
3
Some Extra 2.4 Examples
2) A number is less than 18 or greater than 24.

A: Write a compound inequality that represents the possible
values of the number (Call the number x)
x < 19 OR x > 22

B: Graph the compound inequality on the number line
18
19
20
21
22
23
Section 2.5
Absolute Value
Solving Absolute Value Equations
3)
 Step 1: Set up TWO
equations
x+7=3
-7 -7
x =-4
OR
x+7=-3
-7 -7
x=-10


One exactly as it is written
The second: Change the
sign of the answer
 Step 2: Solve each
equation for the variable
Solving Absolute Value Equations
4)
40  4 x  5  8
-8
-8
32  4 x  5
4
4
8  x 5
 ISOLATE ABS VALUE
FIRST
 Set up TWO equations


One exactly as it is written
The second: Change the
sign of the answer
Solving Absolute Value Equations Cont…
8  x 5
8=x+5 OR -8=x+5
3=x
OR -13=x
 Set up TWO equations


One exactly as it is written
The second: Change the
sign of the answer
 Solve each equation for
the variable
Solving Absolute Value Inequalities
Absolute Value Inequality



Equivalent compound inequality
ax  b  c
-c < ax+b AND ax+b<c
ax  b  c
-c ≤ ax+b AND ax+b≤c
ax  b  c
ax  b  c
ax+b< -c OR ax+b>c
ax+b≤ -c OR ax+b≥ c
Solve the Following
5)
Use the table on the previous slide to write
as an equivalent compound inequality
2x-4 ≤ -6 OR 2x-4≥6
2x ≤ -2
ax  b  c
2x≥10
x≤ -1
Then solve both inequalities for x
x≥5

-2
0
2
ax+b≤ -c OR
ax+b≥ c
4
6
8