Absolute Value Equations

Solving Absolute Value Equations

​Objectives

​- Identify absolute-value equations.

​

- Solve equations in one variable that contain absolute values.

​Absolute value equations are equations where the variable is in an absolute value symbol, like |x-5| = 9. 

Multiple Choice

An absolute value equation is

• an equation that contains a variable in an absolute value

• always going to have two solutions

• always going to have one solution

• impossible to solve

​The solutions are x = 12 and x = -12.

Multiple Choice

Solve for x.

|x| = 7

• X= 7

• X= -7

• X= 7 and X= -7

• No Solution

Multiple Choice

Solve for x.

|x| = -3

• x = 3 and x = -3

• x = 3

• x = -3

• No Solution

​The solutions are x = 1 and x = -15.

Multiple Choice

What would be the correct setup for solving for x?

| x + 3 | = 5

• x + 3 = 5

  and

  x + 3 = -5

• x + 3 = 5

  and

  x - 3 = 5

• x + 3 = -5

  and

  x - 3 = -5

• x + 3 = 5

  and

  -x - 3 = -5

Multiple Choice

Solve for x.

-6 |-2x - 7| = -18

• x = -5 and x = -2

• x = 5 and x = -2

• x = -5 and x = 2

• x = 5 and x = 2

​The solutions are x = 7 and x = -7.

Multiple Choice

solve for z.

|3z|+1=10

• z = -3 and z = 3

• z = 3 and z = 4

• z = -3 and z = 6

• z = -2 and z = 3

​The solutions are x = 10.5 and x = -5.5

Multiple Choice

Solve

∣ 2x + 9 ∣ = 15

• x = -6 and x = 3

• x = -12 and x = 6

• x = 3

• x = -12 and x = 3

​The solution is x = -2

Multiple Choice

Solve for x.

2 | x – 3 | + 8 = 8

• x = 3

• x = -3

• x = -3 and x = 3

• no solution

Multiple Select

An absolute value equation can have which numbers of solutions?

(select all that apply)

• No Solution

• 1 Solution

• 2 Solutions

• 4 Solutions

• 5 Solutions

Multiple Choice

For an absolute value equation to have ONE solution, which of the following should be true?

• |__| = positive number

• |__| = negative number

• |__| = 0

Multiple Choice

For an absolute value equation to have TWO solution, which of the following should be true?

• |__| = positive number

• |__| = negative number

• |__| = 0

Multiple Choice

For an absolute value equation to have NO solution, which of the following should be true?

• |__| = positive number

• |__| = negative number

• |__| = 0

Multiple Choice

Answer the question shown in the box.

• A

• B

• C

• D

Multiple Choice

Answer the question shown in the box.

• A

• B

• C

• D

Multiple Choice

Answer the question shown in the box.

• A

• B

• C

• D

Multiple Choice

Complete the explanation of the error. The student replaced the absolute value with two equations using the positive and negative values of the number on the other side of the equal sign. However, this number was negative.

• An absolute value cannot be equal to a negative number. The equation has no valid solution.

• He should have only used the negative choice, so only

  13/4

  is a valid solution.

• He should have only used the positive choice, so only 27/4 is a valid solution.

• There is no error, so both

  13/4

  and

  27/4

  are valid solutions.

Poll

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