Exploring Solutions in Algebraic Equations

What are the three types of solutions discussed in the video?

• Single solution, double solution, and triple solution

• Positive solution, negative solution, and zero solution

• Finite solution, infinite solution, and no solution

• No solution, one solution, and infinite solutions

In a no solution problem, what happens when you try to solve the equation?

• You get the same value on both sides

• You get different values on both sides

• You get multiple values that satisfy the equation

• You get a single value that satisfies the equation

What is the result when you subtract 2x from both sides in the no solution example?

• 2

• 2x

• 0

• 4

In the one solution example, what is the value of x?

• -3

• 3

• 12

• -12

What is the first step in solving the one solution example?

• Adding 2x to both sides

• Subtracting 2x from both sides

• Multiplying both sides by 2

• Dividing both sides by 2

In the infinite solutions example, what indicates that the equation has infinite solutions?

• The equation has no variables

• The equation has different constants on both sides

• The equation is identical on both sides

• The equation has a single variable

What is the result when you substitute any number into an infinite solutions equation?

• The equation has no solution

• The equation is not satisfied

• The equation is satisfied

• The equation becomes undefined

In the final example, what is the value of x?

• 3

• 9

• 6

• 12

What is the first step in solving the final example?

• Multiplying both sides by 3

• Adding 3 to both sides

• Using the distributive property

• Subtracting 3 from both sides

What should you do after solving an equation to ensure your solution is correct?

• Write down the steps

• Move on to the next problem

• Ask a friend to verify

• Check the solution by substituting it back into the original equation