Unit 3-2 Solving Absolute Value Equations

What's a way to define absolute value?

• The value of a number
• The opposite of a number
• The distance of a number from zero
• The multiplicative inverse of a number

Tags

CCSS.6.NS.C.7C

Solve.
 $\left|8x-42\right|=42$  

•  $x=10.5,\ x=0$  

• Extraneous Solution

•  $x=0$  

•  $x=10.5,\ x=2$  

Solve.
 $\left|6-2x\right|-3=11$  

•  $x=-4,\ x=10$  

•  $x=-4$  

• Extraneous Solution

•  $x=-4.\ x=6$  

Solve.
 $\frac{\left|5x+7\right|}{11}-8=-6$  

•  $x=3,\ x=-\frac{29}{5}$  

•  $x=3$  

•  $x=-\frac{29}{5}$  

•  $x=3,\ x=\frac{29}{5}$  

Solve.
 $\left|2x-5\right|+17=2$  

• Extraneous Solution

•  $x=-5,\ x=10$  

•  $x=-5$  

•  $x=10$  

An extraneous solution is

• not a concern when solving absolute value equations

• an apparent solution that must be rejected because it does not satisfy (work for) the original equation

Solve.
 $\frac{7\left|3x-7\right|-20}{4}=9$  

•  $x=5,\ x=-\frac{1}{3}$  

•  $x=5$  

• Extraneous Solution

•  $x=5,\ x=-3$  

|v + 8| − 5 = 2

• {-1,-15}

• {-1,-5}

• {-15,15}

• Extraneous Solution

−2|−2r − 4| = -12

• {3,1}

• {-3,-1}

• {-3}

• Extraneous Solution

What is the reason that absolute value is always written as a positive?

• Absolute value is talking about numbers so it must be positive.
• Absolute value does not always have to be positive.
• Absolute value is like a clock it has only positive numbers.
• Absolute value is talking about distance, distance is always measured by positive numbers.

Tags

CCSS.6.NS.C.7C