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Copy HW in your planner. Text p. 32, #4-14 evens, 15-24 all

Copy HW in your planner. Text p. 32, #4-14 evens, 15-24 all Be ready to complete the STAR Testing. After STAR Testing, GoFormative.com; define absolute value in your own words. Then solve the following problems. |5| = ? |-7| = ? | -5 + (-9)| = ? -|18| = ?

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Copy HW in your planner. Text p. 32, #4-14 evens, 15-24 all

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  1. Copy HW in your planner. • Text p. 32, #4-14 evens, 15-24 all • Be ready to complete the STAR Testing. • After STAR Testing, GoFormative.com; define absolute valuein your own words. Then solve the following problems. |5| = ? |-7| = ? | -5 + (-9)| = ? -|18| = ? What could ‘x’ be in the following equations? |x| = 10 |x + 2| = 5

  2. Learning Goal • SWBAT solve absolute value equations. SWBAT solve linear equations in one variable

  3. ABSOLUTE VALUE • The distance a number is away from ZERO. Distance is always positive. -5 -4 -3 -2 -1 0 1 2 3 4 5 negative zero positive What is the absolute value of -4? or |-4| |-4| = 4

  4. ABSOLUTE VALUE EQUATION– an equation that contains an absolute value expression. |x| = 4 means the distance ‘x’ is from zero. -4 -3 -2 -1 0 1 2 3 4 The solution to |x| = 4 is 4 and -4 because they are the only numbers whose distance from 0 is 4.

  5. The equation |ax + b| = c where c ≥ 0, is equivalent to the statement: ax + b = c or ax + b = -c

  6. Solve an Absolute Value Equation Solve |x – 3| = 8 Rewrite the absolute value equations as two equations. Then solve each equation separately. x – 3 = -8 or x – 3 = 8 Rewrite as two equations. x – 3+ 3=-8+ 3 x – 3+ 3=8+ 3 Addition or Subtraction property of inequality or or x = -5 x = 11 Simplify. CHECK |x – 3| = 8. |x – 3| = 8. Substitute for x. |-5 – 3| = 8. |11 – 3| = 8. Simplify. 8 = 8. 8 = 8.

  7. Solve an Absolute Value Equation Solve |r – 7| = 9 Rewrite the absolute value equations as two equations. Then solve each equation separately. |r – 7| = 9 Rewrite as two equations. r – 7 = -9 or r – 7 = 9 Addition or Subtraction property of inequality r = -2 or r = 16 Simplify. CHECK |r – 7| = 9. |r – 7| = 9. Substitute for r. |-2 – 7| = 9. |16 – 7| = 9. Simplify. 9 = 9. 9 = 9.

  8. 2x – 7 = 3 First, rewrite the equation in the form ax + b = c. 32x – 7 – 5 = 4 32x – 7 = 9 2x – 7 = 3 Solve an Absolute Value Equation Solve 3|2x – 7| - 5 = 4 Write original equation. Add 5 to each side. Divide each side by3. Next, solve the absolute value equation. Write absolute value equation. 2x – 7 = -3 or2x – 7 = 3 Rewrite as two equations. 2x = 4 or2x = 10 Add 7 to each side. x = 2 or x = 5 Divide each side by 2.

  9. t + 9 = 6 First, rewrite the equation in the form ax + b = c. 4 t + 9 – 5 = 19 4 t + 9 = 24 t + 9 = 6 Solve an Absolute Value Equation Solve 4|t + 9| - 5 = 19 Write original equation. Add 5 to each side. Divide each side by4. Next, solve the absolute value equation. Write absolute value equation. t + 9 = -6 or t + 9 = 6 Rewrite as two equations. t = –15 or t = –3 Addition & subtraction to each side

  10. The equation |ax + b| = c where c ≥ 0, is equivalent to the statement: ax + b = c or ax + b = -c The equation |ax + b| = c where c < 0, is NO SOLUTION.

  11. First, rewrite the equation in the form ax + b = c. Solve an Absolute Value Equation Solve |3x + 5| + 6 = -2, if possible. |3x + 5| + 6 = -2 Write original equation. |3x + 5| + 6 = -2 Subtract 6 from each side. - 6 - 6 |3x + 5| = -8 The equation |ax + b| = c where c < 0, is NO SOLUTION.

  12. First, rewrite the equation in the form ax + b = c. Solve an Absolute Value Equation Solve -9|4p + 2| - 8 = -35, if possible -9|4p + 2| – 8 = -35 Write original equation. -9|4p + 2| – 8 = -35 Add 8 to each side. +8 +8 -9|4p + 2| = -27 Divide each side by -9. |4p + 2| = 3 Write absolute value equation. Rewrite as two equations. 4p + 2 = -3 or 4p + 2 = 3 p = -1¼ or p = ¼ Addition & subtraction to each side

  13. First, rewrite the equation in the form ax + b = c. Solve an Absolute Value Equation Solve |x - 1| + 5 = 2, if possible. |x – 1| + 5 = 2 Write original equation. | x – 1| + 5 = 2 Subtract 5 from each side. -5 -5 | x – 1| = -3 The equation |ax + b| = c where c < 0, is NO SOLUTION.

  14. In a cheerleading competition, the minimum length of the routine is 4 minutes. The maximum length of a routine is 5 minutes. Write an absolute value equation that represents the minimum and maximum lengths.

  15. Text p. 32, #4-14 evens, 15-24 all, 26

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