Solving Linear Equations Concepts

The video tutorial explains how to solve and verify a linear equation in one variable. It begins with an introduction to the concept of solving linear equations by isolating the variable. The tutorial then details the process of simplifying both sides of the equation by clearing parentheses and combining like terms. Next, it covers isolating the variable through addition or subtraction and solving for the variable by division. Finally, the solution is verified by substituting it back into the original equation to ensure correctness.

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

• To find the sum of all coefficients

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

• To eliminate all variables

• To convert the equation into a quadratic equation

What is the first step in simplifying both sides of a linear equation?

• Adding constants

• Multiplying both sides by zero

• Subtracting variables

• Distributing and combining like terms

When distributing -2 in the equation, what is the result of -2 * 8?

• -16

• 16

• 8

• -8

After simplifying, what operation is used to isolate the variable term?

• Division

• Exponentiation

• Multiplication

• Addition or subtraction

What is the result of subtracting 30 from both sides of the equation?

• The equation becomes balanced

• The variable term is isolated

• The equation becomes zero

• The equation becomes a quadratic

What is the final step to solve for the variable x in the equation -2X = 24?

• Add 2 to both sides

• Subtract 2 from both sides

• Divide both sides by -2

• Multiply both sides by 2

What is the solution to the equation -2X = 24?

• 12

• -24

• -12

• 24

How do you verify the solution of a linear equation?

• By graphing the equation

• By substituting the solution back into the original equation

• By checking the solution with a calculator

• By solving a different equation

What is the result of substituting -12 for X in the equation -2 * (X - 8) + 14?

• 75

• 0

• 40

• 54

What does the equation 40 + 14 = 54 verify?

• The equation is quadratic

• The equation is unsolvable

• The solution is correct

• The solution is incorrect