One, Many, No Solution

What is the definition of infinite solutions?

• no matter what number is substituted in for the variable, the equation is ALWAYS true

• no matter what number is substituted in for the variable, the equation will NEVER be true

• there is only ONE number you can plug in for the variable to make the equation true

Does this equation have One, Many (infinite) or No Solution?

-2(x + 3) = -2x - 6

• One Solution

• Many (Infinite) Solutions

• No Solutions

Answer explanation

When you distribute -2 on the right side of the equation, the equation will read: -2x - 6 = -2x - 6

Because both sides of the equation are EXACTLY the same value, no matter what you put in for x, the values will always be equal. This means there is an infinite amout of solutions for this problem.

Does this equation have One, Many (infinite) or No Solution?

-3x + 5 = 5x - 3

• One Solution

• Many (Infinite) Solutions

• No Solution

Answer explanation

You can solve this equation, and x = 1.

This is the only possible solution to this problem, so there is only one solution.

Which of the following equations have many (infinite) solutions? (Check all that apply)

• 3x - 1 = 3x + 1

• -2x + 1 = 1 – 2x

• 3x – 2 = 2x – 3

• 3(x – 1) = 3x – 3

• 2x + 2 = 2(x + 1)

Answer explanation

For each of the correct answers, the value on the left of the equal sign is exactly the same as the value on the right.

Does this equation have One, Many (infinite) or No Solution?

• One Solution

• Many (Infinite) Solutions

• No Solution

Answer explanation

The value on the left (2x - 6) is the exact same value as on the right side of the equal sign, so no matter the value of "x" - both sides will always be equal. This means there is an infinite number of solutions.

Does this equation have One, Many (infinite) or No Solution?

6(x - 11) = 15 - 4x

• One Solution

• Many (Infinite) Solutions

• No Solution

Answer explanation

You can solve this for one value of "x", meaning there is only one possible solution.

Does this equation have One, Many (Infinite) or No Solution?

11x + 3x - 17 = -4x + 4 - 3x

• One Solution

• Many (Infinite) Solutions

• No Solution

Answer explanation

You can solve this for "x" - there is only one value for x.

Which of the equations shown have no solutions?

• 3x – 1 = 3x + 1

• 2x – 1 = 1 – 2x

• 3x – 2 = 2x – 3

• 3(2x – 1) = 2(3x – 1)

• 3(x – 1) = 3x – 2

Answer explanation

In each of the correct responses, the values on either side of the equal sign are not equal to each other.

Does this equation have One, Many (infinite) or No Solution? 2x - 3 = 2x + 7

• One Solution

• Many (Infinite) Solutions

• No Solution

Answer explanation

When you subtract 2x from both sides of the equation, you get -3 = 7.   These values are not equivalent, so there is no possible solution here that would make this equation true.

Does this equation have One, Many (infinite) or No Solution? 5(2x -2) = 2(5x + 5)

• One Solution

• Many (Infinite) Solutions

• No Solution

Answer explanation

When solving this problem, once you eliminate the variable terms from both sides, you are left wiht -10 = 10, and this is NOT a true statement, meaning this equation has NO solution because there is no value that would make this true.