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Absolute Value Equations 3.6 solving equations only Let’s review: • Write a definition for absolute value: Let’s review: • Write a definition for absolute value: • The absolute value is the numbers distance from zero. For example; • /7/ has the same absolute value as • /-7/ because they are both 7 spaces away from zero on a number line. Let’s practice. Simplify the following: • • • • /15/ = -/-7/ = /-2/ = / 12 – (-12) / = What would the value of x be in this case? • /x/ = 3 • Remember: Since the absolute value represents distance, it can never be negative. However, the number inside the absolute value lines can be either positive OR negative • Therefore /x/ has two solutions. The value of x could be either +3 or -3. So how do we use this information to solve an absolute value equation? • Solve /x/ + 5 = 11 • Remember there will be two solutions for the value of x. So how do we use this information to solve an absolute value equation? • Solve /x/ + 5 = 11 • Remember there will be two solutions for the value of x. • Step 1: subtract 5 from both sides. • /x/ + 5 – 5 = 11 - 5 So how do we use this information to solve an absolute value equation? • Solve /x/ + 5 = 11 • Remember there will be two solutions for the value of x. • Step 1: subtract 5 from both sides. • /x/ + 5 – 5 = 11 - 5 • Step 2: Simplify • /x/ = 6 • X is then equal to both 6 and -6 Let’s substitute both values for x back into the equation to check. • • • • Solve /x/ + 5 = 11 If x = + 6 /6/ + 5 = 11 6 + 5 = 11 Let’s substitute both values for x back into the equation to check. • • • • Solve /x/ + 5 = 11 If x = + 6 /6/ + 5 = 11 6 + 5 = 11 • /-6/ + 5 = 11 • 6 + 5 = 11 To solve an equation where an expression is inside the absolute value marks: • Example: • /2p + 5/ = 11 • Step 1: write 2 equations, set one equal to positive 11 and the other equal to negative 11. 2p + 5 = 11 2p + = -11 Solve for p in each equation. • 2p + 5 = 11 Justify each step: Subtract 5 from both sides 2p + 5 - 5 = 11 – 5 2p = 6 Divide both sides by 2 P=3 2p + 5 = -11 Justify each step: Subtract 5 from both sides 2p + 5 - 5 = -11 – 5 2p = - 16 Divide both sides by 2 P = -8 Try these: 1) /c – 2/ = 6 A) 4 & -8 B)8 2) /7d/ = 14 A) 2 B) – 2 C) -4 D)-4 & 8 C) 2 & -2 D) 28 Think Pair Share • Conclusion: • Take 30 seconds and think about our lesson today. Identify for yourself two key things you learned. • Turn to the person near you and share those two new learnings with your partner. Homework • On pages 161-162 • Do problems 1-21 • Justify your steps as you solve the equations. • Write a brief explanation explaining why #18 has no sloution.