Understanding Linear Equations and Long Division

The video tutorial explains how to solve a linear equation by isolating the variable. It begins by discussing the goal of manipulating the equation to have the variable on one side. The tutorial then covers undoing multiplication through division, specifically focusing on dividing by decimals using long division. The process of calculating the quotient is detailed, followed by verifying the solution to ensure accuracy. The tutorial concludes with a successful check of the solution.

What is the primary goal when solving a linear equation?

• To simplify the equation

• To make both sides of the equation equal

• To eliminate all numbers

• To find the value of the variable

What operation is used to undo multiplication in a linear equation?

• Multiplication

• Addition

• Division

• Subtraction

Why do we move the decimal point when setting up long division?

• To make the quotient a whole number

• To simplify the equation

• To make the divisor a whole number

• To make the dividend a whole number

What is the first step in performing long division with decimals?

• Add zeros to the dividend

• Multiply the divisor by 10

• Subtract the divisor from the dividend

• Move the decimal point in the divisor

How many times does 85 fit into 399?

• 3 times

• 4 times

• 5 times

• 6 times

What is the result of 7 multiplied by 85?

• 5950

• 399

• 595

• 340

What does it mean if the difference in long division is zero?

• The division is complete

• The decimal does not terminate

• The division is incorrect

• The divisor is too large

What should the product of 8.5 and 4.7 equal to verify the solution?

• 39.95

• 40.00

• 38.95

• 41.00

What is the solution to the equation 8.5x = 39.95?

• x = 4.6

• x = 4.5

• x = 4.8

• x = 4.7

Why is it important to check the solution of a linear equation?

• To simplify the equation further

• To verify the solution is correct

• To ensure the equation is balanced

• To find a different solution