4.4 Solving Absolute Value Equations Solve and write absolute value equations in one variable

Warm-up Find the equation of the line that goes through (2, -1) and is perpendicular to the line with equation x – 3y = 7. A. B. C. D. A driver’s education consists of a total of 46 hours of classroom instruction, driving, and observation. You must spend 3 times as much time in the classroom as driving, and 4 hours longer driving than observing. How much time do you spend driving? A. B. C. D. 6 hours 10 hours 14 hours 30 hours A football kicker scores 1 point for each extra point and 3 points for each field goal. One season, a kicker made 34 extra points and scored a total of 112 points. How many field goals did the kicker make? A. B. C. D. 13 26 48 78

The absolute value of x can be defined algebraically as follows: The absolute value of a number x, written , is the distance the number is from 0 on the number line. Because distances are always positive or zero, the absolute value of a number cannot be negative. The absolute value of x can be defined algebraically as follows: If x is a positive number then If x is zero then The expression –x represents the opposite of x which when x is negative, -x is positive If x is a negative number then

The absolute value equation where c > 0 can have two possible value that make the statement true: A positive value c and a negative value c. Example. x = 4 or x = -4 No solution

  Solve an absolute value equation 3 – 4x = 11 3 – 4x = -11 -4x = 8 or 3 – 4x = -11 -4x = 8 -4x = -14 x = -2 Check  

  Solve an absolute value equation You must 1st isolate the absolute value on one side of the equation 2x – 8 = 6 or 2x – 8 = -6 2x = 14 2x = 2 x = 7 x = 1 Check  

Write an absolute value equation Write an absolute value equation that has -6 and 2 as a solution. Locate the midpoint on the graph • • -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 The graph of each solution is 4 units from the midpoint, -2. The distance between a number x and -2 on the number line is midpoint distance

Write an absolute value equation Write an absolute value equation that has -3 and 5 as a solution. Find the distance from the midpoint to one of the solutions. Find the midpoint: Larger solution – midpoint = 5 – 1 =4 The distance is 4

Write an absolute value equation A runner has the times of 41.5 seconds and 43.7 seconds for a quarter mile. Write an absolute value equation that has those two times as its solutions. =42.6 43.7-42.6=1.1 The midpoint is at 42.6 which is 1.1 units from each point

What is (are) the solution(s) of A. B. C. D. Check:

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