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Absolute Value Equations Absolute Value Equations: x 4 , is an equation that contains an absolute value expression. The equation x 4 means that the distance between 0 if 4. The solutions of the equation are 4 and -4, because they are the only numbers whose distance from 0 is 4. Solving an Absolute Value Expression The equation ax b c where c 0 is equivalent to the statement ax+b=c or ax+b=-c Solve an absolute value equation: Solve x 3 8 To solve, rewrite the absolute value equation as 2 equations. Then solve each equation separately. x 38 x 3 8 or x 11 x 5 The solutions are 11 and -5. Check your answer by plugging and chugging both numbers. Try This: x 4 3 When solving multi-step equations, you cannot solve work on numbers inside the absolute value symbol until you get all other numbers out of the equations first Example: Solve 32x 7 5 4 First get the absolute value by itself 32x 7 5 4 32x 7 9 2x 7 3 Then solve the absolute value equation: 2x 7 3 2x 10 2x 7 3 or 2x 4 x5 x2 The solutions are 5 and 2. Try This: 4 t 9 5 19 No Solutions: The absolute value of a number is never negative. So, when an absolute value expression equals a negative number, there are no solutions. 3x 5 6 2 Example: 3x 5 8 Because the solution is -8, there are no solutions. Absolute deviations: For a number from a given value is the absolute value of the difference of x and the given value. Absolute Deviation= x givenvalue Example: Before the start of a professional basketball game, a basketball must be inflated to an air pressure of 8 pounds per square inch (psi) with an absolute error of 0.5 psi. find the minimum and maximum acceptable air pressures for the basketball. 0.5 p 8 0.5=p-8 8.5=p or -0.5=p-8 7.5=p The minimum and maximum acceptable pressures are 7.5 psi and 8.5 psi. Try These: 2m5 4 2 3 n 2 7 10 The absolute deviation of x from 7.6 is 5.2. what are the values of x that satisfy the requirement?