Solving Linear Equations with One Variable

The video tutorial explains how to solve linear equations systematically. It begins with an introduction to linear equations, highlighting that they involve variables not raised to a power greater than one. The tutorial then provides four examples, each demonstrating the step-by-step process of solving linear equations. Key steps include moving terms with variables to one side, moving constants to the other, combining like terms, and dividing by the numerical coefficient. The video emphasizes the importance of changing signs when moving terms across the equal sign.

What makes an equation linear?

• It contains decimals.

• The variable is not raised to a power more than one.

• The variable is raised to a power greater than one.

• It contains fractions.

What is the first step in solving the equation -4 = 2x + 6?

• Divide both sides by the numerical coefficient.

• Move all constants to the left.

• Combine like terms.

• Move all terms with the variable to the left.

What happens to the sign of a term when it is moved across the equal sign?

• It remains the same.

• It changes to its opposite.

• It becomes negative.

• It becomes positive.

In the equation -4 = 3x - 2, what is the result after moving all constants to the right?

• -3x = 14 - 2

• -3x = 12

• -4 - 3x = -2

• 3x = -2

What is the final value of x in the equation -4 = 3x - 2?

• -3

• -4

• 3

• 4

In the equation 4x - 3 = 2x + 7, what is the result after moving all terms with the variable to the left?

• 4x - 2x = 5

• 4x - 2x = 3

• 4x - 2x = 10

• 4x - 2x = 7

What is the next step after combining like terms in the equation 4x - 3 = 2x + 7?

• Move all constants to the left.

• Divide both sides by the numerical coefficient.

• Move all terms with the variable to the right.

• Combine like terms again.

In the equation 4x - 2 - x = 5x + 10, what is the result after moving all variables to the left?

• 4x - 2 - x - 5x = 10

• 4x - 2 - x = 5x

• 4x - x - 5x = 10

• 4x - 2 - x = 10

What is the final value of x in the equation 4x - 2 - x = 5x + 10?

• -6

• 5

• -5

• 6

What is the result after combining like terms in the equation 4x - 2 - x = 5x + 10?

• -2x = 10

• 2x = 10

• -2x = 12

• 3x = 12