Solving Absolute Value Equations & Inequalities. Solving Absolute Value Equations & Inequalities. Standard. MM2A1c. Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology. Absolute Value (of x). Symbol lxl - PowerPoint PPT Presentation
Text of Solving Absolute Value Equations & Inequalities
Solving Absolute Value Equations & InequalitiesSolving
Absolute Value Equations & InequalitiesMM2A1c. Solve absolute
value equations and inequalities analytically, graphically, and by
using appropriate technology.
Absolute Value (of x)Symbol lxlThe distance x is from 0 on the
number line.Always positiveEx: l-3l=3 -4 -3 -2 -1 0 1 2
Ex: x = 5What are the possible values of x?
x = 5 or x = -5
To solve an absolute value equation:ax+b = c, where c>0
To solve, set up 2 new equations, then solve each equation.
ax+b = c or ax+b = -c
** make sure the absolute value is by itself before you split to
Ex: Solve 6x-3 = 156x-3 = 15 or 6x-3 = -156x = 18 or 6x = -12x =
3 or x = -2
* Plug in answers to check your solutions!
Ex: Solve 2x + 7 -3 = 8Get the abs. value part by itself
first!2x+7 = 11Now split into 2 parts.2x+7 = 11 or 2x+7 = -112x = 4
or 2x = -18x = 2 or x = -9Check the solutions.
Your Turn: Solve 2x - 5 = 9
How do you solve absolute value inequalities?
First, isolate the absolute value expression on the left side of
the inequalityThen choose the form of your inequality
Rewrite as ax+b < cAnd ax+b > -c,solve for xRewrite asax+b
c Andax + b > -c, solve for xRewrite asax + b > cOrax + b
< -c,solve for xRewrite asax + b cOrax + b -c,solve for x