Absolute Value equations

Absolute Value equations

How to solve

• Get absolute value by itself

• If equal to a negative the answer is no solution

• If not get rid of absolute value by separating into two two equations

• Solve equations like usual

Example:

 $\left|x+3\right|=5$  

Example:

 $-2\left|x+1\right|=10$  

Example:

 $-3\left|2x+1\right|+4\ =1$  

Multiple Choice

Solve for x
l 5x l = 40

• x = 8 and x =-8
• x = 35 and x = -35
• Only x = 8
• No Solution

Multiple Choice

| x – 3 |= 0

• 3
• -3
• {-3, 3}
• no solution

Multiple Choice

Evaluate each expression.
| x + 9 | = -5

• -14
• -4
• {-14, -4}
• no solution

Multiple Choice

Solve for x
l 2x−1 l = 9

• x = 5 and x =-4
• x = 5 and x = -5
• Only x = 5
• No Solution

Multiple Choice

Solve for x
l 4x−3 l = 17

• x = 5 and x =-3.5
• x = 0 and x = -5
• x = 10 and x = -10
• No Solution

Multiple Choice

Solve for x
l 3x + 2 l = 5

• x = -2.333... and x = 1
• x = 4 and x = 8
• x = 0
• No Solution

Multiple Choice

Solve for x
l 2x−1 l +4 = 8 

• x = 2.5 and x = -1.5
• x = 2 and x = -1
• x = -2 and x = 9
• No Solution

Multiple Choice

Solve for x
l x−6 l + 4= 10

• x = 12 and x = 0
• x = 3 and x = -3
• x = -12 and x = 0
• No Solution

Multiple Choice

Solve for x
3 l 4w−1 l −5 = 10

• x = 1.5 and x =-1
• x = -1.5 and x = 1
• x =1 and x = -1
• No Solution

Multiple Choice

Solve for x
2 lx−4l+8=18

• x = 9 and x =-1
• x = 1 and x = -9
• x= 4 and x = -2
• No Solution