Understanding Solutions of Equations

In this video, Mr. J explains how to determine if a number is a solution to an equation by plugging it in and checking if it satisfies the equation. He provides examples, starting with a simple equation x - 8 = 4, where he tests if x = 15 or x = 12 is a solution. He then moves on to a more complex example involving multiple equations to see if W = 9 is a solution. The video concludes with a summary of the method: plug in the number and see if it works.

What is the basic method to determine if a number is a solution to an equation?

• Solve the equation for the variable.

• Plug the number into the equation and check if it satisfies the equation.

• Use a calculator to find the solution.

• Graph the equation and see if the number is on the line.

In Example 1, what is the result when x = 15 is plugged into the equation x - 8 = 4?

• x = 15 is less than the solution.

• x = 15 satisfies the equation.

• x = 15 does not satisfy the equation.

• x = 15 is greater than the solution.

Which value of x satisfies the equation x - 8 = 4?

• x = 10

• x = 12

• x = 15

• x = 20

For the equation W / 3 = 3, does W = 9 satisfy the equation?

• W = 9 is too small.

• W = 9 is too large.

• No, W = 9 does not satisfy the equation.

• Yes, W = 9 satisfies the equation.

What operation should be performed first when checking if W = 9 satisfies 2W + 7 = 25?

• Addition

• Division

• Subtraction

• Multiplication

Does W = 9 satisfy the equation 2W + 7 = 25?

• Yes, it satisfies the equation.

• No, it does not satisfy the equation.

• It is greater than the solution.

• It is less than the solution.

In the equation 31 = 42 - W, what is the result when W = 9 is plugged in?

• W = 9 is too large.

• W = 9 is too small.

• The equation is satisfied.

• The equation is not satisfied.

Which of the following equations is not satisfied by W = 9?

• 2W + 7 = 25

• W + 5 = 14

• 31 = 42 - W

• W / 3 = 3

What is the final step to determine if a number is a solution to an equation?

• Ensure the number is an integer.

• Compare the number to zero.

• Verify if the number satisfies the equation.

• Check if the number is positive.

What is the main takeaway from the video on determining solutions of equations?

• Use trial and error with random numbers.

• Graph the equation for a visual solution.

• Plug in the number and check if it satisfies the equation.

• Always use a calculator.