Absolute Value Equations

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

Solve the following equation.

| 2x + 3 | = | 3x |

• No Solution

• {-14, -4}

What is the first step to solve the following equation?

-2|x + 3| = -10

• Set up 2 equations

  -2(x + 3) = 10

  -2(x + 3) = -10

• Add 2 to both sides

• Subtract 3 from both sides

• Divide by -2 on both sides

• No Solution

Solve for x.

| x – 3 |= 0

• 3
• -3
• {-3, 3}
• no solution

• {-7, 3}

What is the FIRST step to solving the equation:

|x + 1| = 4

• Set up 2 equations

  x + 1 = 4

  x + 1 = -4

• Subtract 1 on both sides

• Set up 2 equations:

  x + 1 = 4

  x - 1 = 4

• Add 1 to both sides

What is the first step to solve the following equation?

|2x - 1| = -5

• Add 1 to both sides

• Set up 2 equations:

  2x - 1 = 5

  2x - 1 = -5

• No Solution

• Divide by 2 on both sides.

Solve for n.

 |−2n| + 10 = −50

• {30, -30}
• {20,-20}
• {-5,5}
• No Solution

When do you set up 2 equations?

|x + 2| + 3 = 4

• That is the first step.

• After you subtract 3 from both sides.

• After you add 2 and 3.