Solving Linear Equations with Decimals

The video tutorial explains how to solve a linear equation in one variable by isolating the variable. It begins by addressing the presence of decimals in the equation and suggests clearing them by multiplying by a power of 10. The tutorial then demonstrates how to isolate the variable by moving terms to one side of the equation and solving the resulting two-step equation through subtraction and division. The solution is presented as a decimal, and the tutorial concludes with a summary of the steps taken.

What is the primary goal when solving a linear equation in one variable?

• To eliminate all numbers from the equation

• To isolate the variable on one side

• To convert the equation into a quadratic form

• To ensure the equation has no decimals

Why is it important to clear decimals in a linear equation?

• To convert the equation into a fraction

• To make the equation more complex

• To change the variable

• To simplify calculations and avoid errors

What is the effect of multiplying a term by 100 in the context of clearing decimals?

• It divides the term by 100

• It adds two zeros to the term

• It moves the decimal point two places to the right

• It moves the decimal point two places to the left

When isolating the variable, why might one choose to subtract 280X from both sides?

• To make the variable term negative

• To ensure the variable term is on the right side

• To eliminate the variable completely

• To have the variable term on the left side

What is the result of subtracting 1820 from both sides of the equation?

• The equation becomes a quadratic equation

• The equation becomes a one-step equation

• The equation is simplified to negative 80X equals a difference

• The equation is solved completely

How do you determine the sign of the result when adding integers with different signs?

• By always taking the sign of the first number

• By taking the sign of the number with the larger absolute value

• By making the result always positive

• By making the result always negative

What is the final step in solving the equation for X?

• Subtracting 80 from both sides

• Dividing both sides by negative 80

• Multiplying both sides by 80

• Adding 80 to both sides

Why is the solution given as a decimal in the final step?

• Because it simplifies the equation

• Because decimals are easier to understand

• Because fractions are not allowed

• Because the original equation contained decimals

What is the solution to the equation after performing the division?

• 21.5

• 19.8

• 18.7

• 20.9

What is the significance of a negative divided by a negative in the context of this problem?

• It results in an undefined solution

• It results in zero

• It results in a positive solution

• It results in a negative solution