Solving Linear Equations and Verification

The video tutorial explains how to solve a multi-step linear equation by isolating the variable. It begins with distributing terms to eliminate parentheses, followed by simplifying the equation. The process involves undoing subtraction and multiplication to isolate the variable x. The solution is verified by substituting back into the original equation. The tutorial concludes with a brief preview of future examples.

What is the primary goal when solving a linear equation?

• To find the value of the variable

• To eliminate all numbers

• To isolate the variable on one side

• To make both sides of the equation equal

What is the first step in solving the given equation?

• Adding numbers to both sides

• Distributing the number to eliminate parentheses

• Dividing both sides by a number

• Subtracting numbers from both sides

After distributing, what is the simplified form of 4 times (3x - 7)?

• 4x - 7

• 12x - 28

• 12x + 28

• 3x - 7

What operation is performed to isolate the variable after simplifying the equation?

• Subtraction

• Multiplication

• Division

• Addition

What is the result of adding 28 to both sides of the equation?

• 12x = -72

• 12x = 0

• 12x = -16

• 12x = 16

What is the final step to solve for x in the equation 12x = -16?

• Divide both sides by 12

• Subtract 12 from both sides

• Add 12 to both sides

• Multiply both sides by 12

What is the simplified form of the solution -16/12?

• -4/3

• -8/6

• -2/1

• -3/4

How do you verify the solution of the equation?

• By checking if the solution satisfies the original equation

• By solving a different equation

• By multiplying the solution by 2

• By adding the solution to the original equation

What is the result when substituting x = -4/3 back into the original equation?

• The equation becomes 0 = 0

• The equation becomes -44 = -44

• The equation becomes -28 = -28

• The equation becomes 44 = 44

What does it mean if the original equation is satisfied after substitution?

• The equation is invalid

• The solution is correct

• The equation needs to be solved again

• The solution is incorrect