Solving Equations and Absolute Value Equations

How many solutions does the equation have?

|-5c| = 0

• no solution

• one solution

• two solutions

solve for t.

|t - 8| + 4 = 11

• 1, 15

• -23, 7

• 15

• 15, -15

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?

-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

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.

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 v:

|v + 8| − 5 = 2

• {-1,-15}

• {-1,-5}

• {-15,15}

• No Solution

Solve for a:

|2a - 10| = 6

• a = 8, a = 5

• a = 2

• a = 8

• a = 8, a = 2

Solve for x:

|−4 + 5x| = 16

• {16/5,12/5}

• {4,-5}

• {-12/5, 4}

• 4

Solve for r:

−2|−2r − 4| = -12

• {3,1}

• {-3,-1}

• {-3}

• No Solution