Transcript Solving Inequalities and Absolute Value Equations

SOLVING INEQUALITIES
AND ABSOLUTE VALUE
EQUATIONS
INTRODUCTION LESSONS ALGEBRA 2 – LESSON 1
Solving inequalities follows the same procedures as solving
equations.
There are a few special things to consider with inequalities:
We need to look carefully at the inequality sign.
We also need to graph the solution set.
>
<
greater than
less than
> greater than or equal
< less than or equal
●Sometimes you may have to reverse
the direction of the inequality sign!!
That only happens when you
multiply or divide both sides of the
inequality by a negative number.
How to graph the solutions of inequalities
x > Graph any number greater than. . .
open circle, line to the right
x < Graph any number less than. . .
open circle, line to the left
x > Graph any number greater than or equal to. . .
closed circle, line to the right
x < Graph any number less than or equal to. . .
closed circle, line to the left
Solve and graph on a number line.
A) 2x+3>x+5
B) -2c - 11>23
C) 3(r-2)<2r+4
Solve and graph on a number line.
D) 3x + 5 > -2
3
E)
7x + 3 < 18x – 30
F) 2x > x + 1 + x
Solving Absolute Value Equations
• First, isolate the absolute value expression.
Remember Absolute Value is always positive!
• Set up two equations to solve.
Consider the equation | x | = 3. The equation has two solutions since x can equal 3 or -3.
• 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!!!
Solve |x + 8| = 3
Solve each absolute value equation.
A) |y + 4| - 3 = 0
B) |3d - 9| + 6 = 0
C) 3|x - 5| = 12
Solve each absolute value equation.
D) 6|5x + 2| = 312
E) 3|x + 2| -7 = 14
F) |x – 2| = 2x - 10