Types of Solutions in Equations

What characterizes an equation with one solution?

• The variables cancel out, resulting in a false statement.

• The solution comes out to a variable equaling a specific number.

• All real numbers make the equation true.

• The equation simplifies to a true statement without variables.

Which of the following equations have ONE solution (different variable terms on both sides of the equation)?

• 2x + 6 = -2x + 8

• x + 9 = x + 6

• 3x - 6 = 3(x - 2)

• 3x + 4 = 4 - 3x

• 2x - 7 = 2(x - 7)

Which of the following have one solution?

• 3x + 6 = -3x - 6

• 5x + 2 = -x + 14

• -x + 5 = -(x + 5)

• 2x - 7 = 2x - 9

What is the outcome when an equation has no solution?

• The variables cancel out, and the final statement is false.

• The variables cancel out, and the final statement is true.

• The equation simplifies to x = 0.

• There is only one specific value for the variable.

Which of the following equations have NO SOLUTION (are not true for any value of x)?

• x + 2 = x + 6

• 2x + 8 = 2x + 10

• 2x + 5 = 2(x + 5)

• x + 2 = -x + 6

• 2x + 8 = -2x + 10

Organize these options into the right categories

Groups:

(a) One solution

,

(b) No Solution

• 4x + 3 = 3x - 3

• x + 3 = x - 3

• x + 3 = -x + 3

• 2x + 4 = 2(x + 4)

• 2x + 7 = -2x + 15

• x + 9 = x - 10

Which statement describes an equation with infinite solutions?

• Only one specific value makes the equation true.

• There is no value that makes the equation true.

• All real numbers make the equation true.

• The variables remain on both sides of the equation.

Organize these options into the right categories

Groups:

(a) Infinitely Many Solutions

,

(b) One Solution

,

(c) No Solutions

• 2x + 5 = 2x + 8

• 2x + 5 = -2x - 8

• 2x + 10 = 2(x + 5)

Categorize the equations.

Groups:

(a) One Solution

,

(b) Infinitely Many Solutions

,

(c) No Solution

• 3x + 5 = -3x + 5

• 2x + 10 = 2x - 10

• 2x + 10 = 2x + 10

How many solutions does the equation 6(2x + 2) - 6x = 12 + 6x have?

• One solution

• No solution

• Infinite solutions

• Two solutions