Verifying Solutions in Equations

The video tutorial focuses on verifying solutions to equations. It begins with an introduction to the concept of verifying solutions by substituting values into equations and checking if both sides are equal. The tutorial then provides three examples: verifying M = 10/3 in a fraction equation, checking if N = -3 is a solution, and modeling consecutive integers to verify solutions. Each example is explained step-by-step, demonstrating the process of substitution and evaluation to determine if a given value is a solution.

What is the first step in verifying if a number is a solution to an equation?

• Check if the equation is linear.

• Graph the equation.

• Substitute the number into the equation.

• Solve the equation for the variable.

When verifying the solution M = 10/3 for the equation 9M - 19 = 3M + 1, what is the value of the left side after substitution?

• 10

• 30

• 11

• 19

In the equation 9M - 19 = 3M + 1, what operation is performed after substituting M = 10/3 to simplify the left side?

• Division

• Addition

• Subtraction

• Multiplication

What is the result of adding 1 to 30/3 in the verification process of the equation 9M - 19 = 3M + 1?

• 10

• 11

• 12

• 13

For the equation 5 + (-8N) = 29, what is the result of substituting N = -3?

• 29

• 0

• 5

• 24

What is the result of multiplying -8 by -3 in the equation 5 + (-8N) = 29?

• -24

• 24

• -29

• 29

How do you define the smallest integer in the equation modeling three consecutive integers summing to 36?

• N

• N + 2

• 3N

• N + 1

What is the simplified form of the equation for the sum of three consecutive integers equaling 36?

• N + 2 = 36

• 3N + 3 = 36

• 3N = 36

• N + 1 = 36

In the equation 1/2M - 4 = 5, what is the first step to verify a guess for M?

• Add 4 to both sides.

• Multiply both sides by 2.

• Substitute the guess into the equation.

• Divide both sides by 2.

What is the purpose of verifying multiple guesses for an equation?

• To check if any guess satisfies the equation.

• To find the largest solution.

• To identify all possible solutions.

• To confirm the equation is correct.