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

X= 7

X= -7

X= 7 and X= -7

No Solution

x = 3 and x = -3

x = 3

x = -3

No Solution

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

x = -5 and x = -2

x = 5 and x = -2

x = -5 and x = 2

x = 5 and x = 2

z = -3 and z = 3

z = 3 and z = 4

z = -3 and z = 6

z = -2 and z = 3

x = -6 and x = 3

x = -12 and x = 6

x = 3

x = -12 and x = 3

x = 3

x = -3

x = -3 and x = 3

no solution

No Solution

1 Solution

2 Solutions

4 Solutions

5 Solutions

|__| = positive number

|__| = negative number

|__| = 0

|__| = positive number

|__| = negative number

|__| = 0

|__| = positive number

|__| = negative number

|__| = 0

A

B

C

D

A

B

C

D

A

B

C

D

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.