Transcript Absolute Value Equations - San Jacinto Unified School District

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.
•
•
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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.