Transcript Alg 1.6 1.6 Absolute value equations and inequalities

Do Now
1. Solve 2x+3>x+5
X>2
2. Solve - c - 11>23
C < - 34
3. Solve 3(-r-2)<2r+3
Getting Started

You are riding an
elevator and decide you
want to see how far it
travels in 10 minutes.
The table below shows
the floors it travels to
over time. How far in
feet did the elevator
travel? (assume 10’
between floors) Trip 1
Floors
+8
2
3
4
5
-6
+9
-3
+7
Chapter 1.6
Absolute Value Equations and
Inequalities
Target: I can
Write and solve equations and inequalities
involving absolute value
Solving Absolute Value Equations
Absolute value is denoted by the bars |3|.
Absolute value represents the distance a
number is from 0. Thus, it is always
positive.
 |8| = 8 and |-8| = 8
Solving absolute value equations
• First, isolate the absolute value expression.
• Set up two equations to solve.
• For the first equation, drop the absolute
value bars and solve the equation.
• For the second equation, drop the bars,
negate the opposite side, and solve the
equation.
• Always check the solutions.
Solving Absolute Value Inequalities
• Solving absolute value inequalities is a
combination of solving absolute value equations
and inequalities.
• Rewrite the absolute value inequality.
• For the first equation, all you have to do is
drop the absolute value bars.
• For the second equation, you have to negate
the right side of the inequality and reverse the
inequality sign.
6|5x + 2| = 312
• Isolate the absolute value expression by dividing by 6.
6|5x + 2| = 312
|5x + 2| = 52
• Set up two equations to solve.
5x + 2 = 52
5x = 50
x = 10
or
5x + 2 = -52
5x = -54
x = -10.8
•Check: 6|5x + 2| = 312
6|5(10)+2| = 312
6|52| = 312
312 = 312
6|5x + 2| = 312
6|5(-10.8)+ 2| = 312
6|-52| = 312
312 = 312
3|x + 2| -7 = 14
• Isolate the absolute value expression by adding 7 and dividing by 3.
3|x + 2| -7 = 14
3|x + 2| = 21
|x + 2| = 7
• Set up two equations to solve.
x+2=7
x=5
or
•Check: 3|x + 2| - 7 = 14
3|5 + 2| - 7 = 14
3|7| - 7 = 14
21 - 7 = 14
14 = 14
x + 2 = -7
x = -9
3|x + 2| -7 = 14
3|-9+ 2| -7 = 14
3|-7| -7 = 14
21 - 7 = 14
14 = 14
Solve: |2x + 4| > 12
2x + 4 > 12
2x > 8
x>4
or
2x + 4 < -12
2x < -16
x < -8
or
x < -8 or x > 4
-8
0
4
Solve: 2|4 - x| < 10
|4 - x| < 5
4-x<5
-x<1
x > -1
and
and
4 - x > -5
- x > -9
x<9
-1 < x < 9
-1 0
9
Homework
Assignment – p. 46 10 – 30 odds
Challenge – #82