Solving Absolute Value To solve (when the absolute value is by itself), split into two equations: • One with a positive 6 • The other with a negative 6 Then solve each individually
Check for Understanding What is the solution to |3x + 1| = - 5 There is no solution. The result of an absolute equation can never be negative. But what about the second equation that we write using anegative sign? There are 2 differences. 1st: The originalequation is always a positive. For example, |3x + 1| = 5 2nd: Given |3x + 1| = 5, the second equation is really written as: - |3x + 1| = 5; The opposite of the absolute value....So, the opposite of -|3x - 1| = 5; Therefore, -3x = 6; -3x/-3 = 6/-3; x = 2 Our shortcut is to put the negative on the other side, because it works out the same. If the original absolute value equation equals a negative number, there is no solution.
Guided PracticeEx.1: 3|x - 1| + 1 = 10 For the Positive Value: 3|x - 1| + 1 = 10 1. Goal: Isolate the -1 -1 absolute value 3|x - 1| = 9 a. Subtract 1 |x - 1| = 3 b. Divide by 3 x=4 c. add 1. x = 4 For the Negative Value: 3|x - 1| + 1 = 10 1. Goal: Isolate the absolute -1 -1 value 3|x - 1| = 9 a. Subtract 1 |x - 1| = -3 b. Divide by 3 x = -2 c. Then Change sign to negative d. add 1; x = -2
SummaryWhat are the steps to solve an absolute valueequation?1. Is the Absolute Value alone (isolated) on one side?2. Split the Absolute Value into two equations3. Change the sign on the right only after isolating the absolute value.4. Solve each equation individually5.Check your answers by plugging them in!
Warm-UpEmergency Khan Academy Questions: Combining Like Terms with Distribution
Warm-Up Equations: Build from the ground up1. Write and solve an equation with distribution.2. Write and solve an equation with distributionand a variable on each side. The answer must be awhole number. Absolute Value 3. |x/5| = 2 3. |x/5| = 2; |x/5| = - 2
Warm-Up 4. 3|x + 6| + 12 = 18 Solve for the positive first Goal: Get the absolute value by itself on the left side. a. Subtract 12 from each side b. divide by 3 c. Subtract 6 from each side -4 d. x = ? Solve for the opposite next Goal: Get the absolute value by itself on the left side before changing the sign on the right side. a. Subtract 12 from each side b. divide by 3c. We have |x + 6| = 2; Now we can change the equation to: x + 6 = -2d. Solving, we get x = 2. The solution is x = - 4, or x =-8
Class Work: Handout: Pleaseuse separate page for NUMBEREDscratch paper.