Harkeerit&Kyra

Harkeerit&Kyra

• 1.
  What is anAbsolute Value?An absolute value of a number is its distance from zero.Think of it in terms of a number line.Each blue dot is three units away from zero.Therefore, the absolute value of 3, as well as -3, is 3.
• 2.
  How To Writean Absolute Value.When writing an absolute value, use bars. For example:The absolute value of |5| = 5The absolute value of |-11| = 11 Therefore, | x | = 4 has two possible values, 4 and -4.
• 3.
  How to Solvean Absolute Value EquationSeparate the equation into two different cases. One will be the positive version and the other will be the negative. Then continue to solve by using algebra.Ex. | x + 2 | = 7(x + 2) = 7x+ 2 = 7x= 5OR–(x + 2) = 7   –x – 2 = 7–9 = x Therefore, the solutions are x = 5, -9.
• 4.
  How to Solvean Absolute Value Equation ContinuedTo check your answer, plug the numbers back into the equation.| (5) + 2 | = 7 | 7| = 7| (-9) + 2 | = 7 | -7 | = 7
• 5.
  How to Solvean Absolute Value Equation Continued TRY:| x – 1 | = 2x + 1 Solution:(x – 1) = 2x +1 x – 1 = 2x + 1 - 2x + 1 - 2x +1  - x = 2 x = -2 OR - (x – 1) = 2x +1 - x + 1 = 2x + 1 -2x -1 -2x -1 -3x = 0  x = 0Check:| (0) – 1 | = 2(0) + 1| -1| = 1 | (-2) – 1 | = 2(-2) + 1| -3 | = -3REJECT
• 6.
  Try!(Hint: isolate theabsolute-value expression)| 2x – 3 | – 4 = 3Solution:(2x – 3) = 7         2x– 3 = 7       2x= 10 x= 5  OR – (2x – 3) = 7 –2x + 3 = 7           –2x = 4            x = –2 Check answer
• 7.
  Basic GraphsThe mostbasic graph is y = |x|It forms a V shape because there are restrictions. The absolute value cannot be negative, therefore, the y coordinates are greater or equal to 0.
• 8.
  Basic Graphs Continued The following graph shows y = -|x|y = |x + h| the graph will move h units to the lefty = |x - h| the graph will move h units to the righty = |x| + k the graph will move up k unitsy = |x| - k the graph will move down k unitsTo graph equations like | x + 2 | = 7:Set y1 = | x + 2 |Then set y2 = 7