Solving Linear Equations and Verification

The video tutorial explains how to solve a multi-step equation by simplifying both sides, isolating the variable, and verifying the solution. It begins with an introduction to the equation, followed by combining like terms to simplify it. The tutorial then demonstrates isolating the variable term and solving for x. Finally, the solution is verified by substituting the value back into the original equation.

What is the main goal when solving an equation?

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

• To eliminate all variables from the equation

• To simplify the equation as much as possible

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

What is the first step in simplifying the equation 4x + 6x + 8 - x - 3 = 32?

• Divide by the coefficient of x

• Multiply to clear fractions

• Combine like terms

• Add constants on both sides

After combining like terms, what does the left side of the equation simplify to?

• 7x + 5

• 8x + 5

• 9x + 5

• 10x + 5

What operation is used to isolate the variable term in the equation 9x + 5 = 32?

• Divide both sides by 5

• Multiply both sides by 5

• Subtract 5 from both sides

• Add 5 to both sides

What is the result of subtracting 5 from both sides of the equation 9x + 5 = 32?

• 9x = 22

• 9x = 32

• 9x = 37

• 9x = 27

What is the final step to solve the equation 9x = 27?

• Multiply both sides by 9

• Divide both sides by 9

• Add 9 to both sides

• Subtract 9 from both sides

What is the value of x in the equation 9x = 27?

• x = 4

• x = 2

• x = 3

• x = 5

How do you verify the solution x = 3 in the original equation?

• By substituting x = 3 into the equation and checking if both sides are equal

• By graphing the equation and checking the intersection

• By substituting x = 3 into a different equation

• By solving the equation again with x = 3

What is the result of substituting x = 3 into the original equation?

• The left side equals 30

• The left side equals 32

• The left side equals 36

• The left side equals 34

What does the verification step confirm about the solution x = 3?

• It confirms that x = 3 is correct

• It confirms that x = 3 is incorrect

• It confirms that x = 3 is one of many solutions

• It confirms that x = 3 is an approximation