Solving Absolute Value Equations
Step 1. Undo the operations outside absolute value bars, so that the problem looks like this.
Step1a. If the problem is now a situation where it is |expression| = -#, then the answer is null set.
Step 2. Split the above problem into two equations similar to the diagram below. Solve for the unknown in each equation. (Notice that the absolute value bars have been dropped.)
Directions: Please solve for the unknown in the following absolute value equation.
3|2x-4|+2=62
Step 1. Notice that the absolute value quantity is not isolated on one side of the equation. We must subtract two on both sides then divide by three on both sides to rectify this.
3|2x-4|+2=62
3|2x-4|=60
|2x-4|=20
Step 2. Now that the problem is consistent with the diagram above, we can split the problem into two equations and solve them.
|2x-4|=20 becomes
2x-4=20 & 2x-4=-20
2x=24 & 2x=-16
x=12 & x=-8
Directions: Please solve for the unknown in the following absolute value equations. If there is no solution, please indicate so by stating "null set".
1. |2y-7|=9 2. |-3b|=9 3. |2x-10|=14
4. |9c|+6=15 5. -5|6r|=-45 6. 4|8-2y|+6=30
7. 4|6-x|=20 8. -7|2x+21|-7=42 9. 1/2|4+2g|=20
10. 5-|2-3x|=-12
Directions: Please answer the following word problem.
11. The distance of a number from zero doubled and then decreased by ten is thirty. What number(s) did we start with?
Directions: Please write 1-2 paragraphs that thoroughly address the following.
1. Consider the following statement. "Taking the absolute value of a number can not yield a negative number because it is a distance and distance must be positive." This statement is true. This being the case, why isn't the answer to problem 10 above "null set"?
1. EMR (Exercises in Math Readiness)
2. Absolute value problems on mathnotes.com Note: The lessons on the mathnotes site require plug-in found on another web Page. Click here to get to it. Read the instructions, and install Interact Math. Once you do this click the mathnotes.com link. Try Exercise 3.
