Solving Linear Equations Concepts

This video tutorial demonstrates how to solve a linear equation with variable terms on both sides. It covers the process of creating equivalent equations by performing the same operations on both sides, simplifying the equation, isolating the variable, and solving for it. The tutorial concludes with verifying the solution by substituting it back into the original equation.

What is the main goal when solving a linear equation with variables on both sides?

• To ensure the equation has no fractions.

• To make both sides of the equation identical.

• To eliminate all numbers from the equation.

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

Why is it important to perform the same operation on both sides of an equation?

• To make the equation more complex.

• To eliminate variables.

• To simplify the equation.

• To keep the equation balanced.

What is the first step in solving a linear equation?

• Adding the same number to both sides.

• Isolating the variable on one side.

• Simplifying each side by clearing parentheses and combining like terms.

• Multiplying both sides by the same number.

When isolating the variable term, what operation is performed to move terms from one side to the other?

• Addition or subtraction

• Exponentiation

• Division

• Multiplication

What happens to the equation when you subtract the same term from both sides?

• The equation is solved.

• The equation becomes unbalanced.

• The equation remains equivalent.

• The equation becomes more complex.

After isolating the variable term, what is the next step to solve for the variable?

• Square both sides of the equation.

• Subtract a constant from both sides.

• Multiply or divide to isolate the variable.

• Add a constant to both sides.

What is the result of dividing both sides of an equation by the same non-zero number?

• The equation is solved.

• The equation becomes more complex.

• The equation remains equivalent.

• The equation becomes invalid.

What is the final solution for n in the given equation?

• n = -19

• n = -38

• n = 38

• n = 19

What is the purpose of verifying the solution of a linear equation?

• To ensure the solution is a whole number.

• To check if the solution satisfies the original equation.

• To make sure the solution is positive.

• To confirm the equation has no fractions.

How do you verify that your solution to a linear equation is correct?

• By simplifying the solution further.

• By substituting the solution back into the original equation.

• By checking if the solution is a whole number.

• By ensuring the solution is positive.