Absolute Value Equations and Inequalities
A.CED.1 Create equations and inequalities in one variable and...solve problems...Also A.SSE.1,A.SSE.1.b
Student Goals:
Students will be able to understand how to solve an absolute value equation and solving an absolute value inequality equation.
Solving Absolute Value Equations
We have the form of |A|=b and b>0. In order to solve an equation like this, we need to solve two equations such as A=b and A=-b.
When we try to solve absolute value equations, we have to create two separate equations. One of the equations is positive (on the left) and one of them is negative (on the right).
We can take |3x+4|=15 and set up two different equations. We are going to remove the absolute value signs, and then set whatever was inside them equal to 15 and -15.
Once we set up the two equations, the positive and the negative, we solve them as we normally would for regular equations.
Follow this example
Steps for solving the positive
Remove the parenthesis by distributing the positive 1 to each term in the parenthesis
Subtract 2 from both sides
Divide 2 to both sides
Steps for solving the negative
Remove the parenthesis by distributing the negative 1 to each of the terms inside the parenthesis
Add 2 to both sides
Divide both sides by -2 (Note: when you multiply or divide an inequality by a negative number, you need to change the direction of the the inequality. < to > and > to < )
Graphing the solution
This would be the solution set for our problem. When we read the solution, we read it as "x is greater than or equal to 2" and "x is less than or equal to negative 4" . What this means is we need to draw out the number, plot those two critical numbers, and then draw the arrows.
Try these examples. Solve these and click the
|2y+10| = 20
|2x-2| > 8
|3x+9| < 36
External Resource
Absolute value inequalities
External Resource
Absolute value equations