Verifying and Simplifying Linear Equations

This video tutorial explains how to solve linear equations in one variable by simplifying them. It covers two examples, demonstrating the process of combining like terms, isolating the variable, and verifying the solution. The tutorial emphasizes the importance of simplifying equations by eliminating parentheses and combining terms, and it provides a detailed walkthrough of each step involved in solving and verifying the equations.

What does it mean to solve a linear equation?

• To find the value of the variable that makes the equation true

• To rewrite the equation in a different form

• To eliminate all variables from the equation

• To add more variables to the equation

In the equation 8x - 14 - 7x + 18 = -10, what are the like terms on the left side?

• -14 and 18

• Both b and c

• 8x and -7x

• 8x and 18

What is the simplified form of the equation 8x - 14 - 7x + 18 = -10?

• x + 4 = -10

• x - 4 = -10

• x - 4 = 10

• x + 4 = 10

How do you verify the solution x = -14 for the equation 8x - 14 - 7x + 18 = -10?

• By substituting x = -14 into the simplified equation

• By checking if x = -14 is a positive number

• By substituting x = -14 into the original equation

• By solving a different equation

What is the first step in solving the equation 12(x - 5) - 11x = -7 + 5?

• Combine like terms on the right side

• Add 5 to both sides

• Subtract 11x from both sides

• Distribute 12 on the left side

After distributing and combining like terms, what is the simplified form of 12(x - 5) - 11x = -7 + 5?

• x + 60 = -2

• x + 60 = 2

• x - 60 = -2

• x - 60 = 2

What operation is used to isolate x in the equation x - 60 = -2?

• Divide both sides by 60

• Multiply both sides by 60

• Add 60 to both sides

• Subtract 60 from both sides

How do you verify the solution x = 58 for the equation 12(x - 5) - 11x = -7 + 5?

• By checking if x = 58 is a positive number

• By substituting x = 58 into the original equation

• By substituting x = 58 into the simplified equation

• By solving a different equation

What is the result of simplifying 12 times 53 minus 11 times 58?

• 0

• -2

• 2

• 1

What is the final step in verifying the solution for the second example?

• Subtract the solution from both sides

• Multiply the solution by both sides

• Add the solution to both sides

• Check if the left side equals the right side