Solving Linear Equations with Variables on Both Sides

This video tutorial demonstrates how to solve a linear equation with variables on both sides, emphasizing the importance of performing equivalent operations on both sides. The process involves simplifying both sides by clearing parentheses and combining like terms, isolating the variable on one side, and solving for the variable by undoing operations. The solution is verified by substituting the value back into the original equation to ensure both sides are equal.

What is the first step in solving a linear equation with variables on both sides?

• Simplify both sides by clearing parentheses and combining like terms

• Multiply both sides by zero

• Add a constant to both sides

• Divide both sides by a variable

When simplifying the left side of the equation, what operation is performed with -2?

• It is distributed across the terms inside the parentheses

• It is subtracted from the constant

• It is added to the variable

• It is divided by the variable

How do you isolate the variable term on one side of the equation?

• By adding a constant to both sides

• By multiplying both sides by the variable

• By adding or subtracting terms to move the variable to one side

• By dividing both sides by a constant

What is the purpose of adding 8 to both sides of the equation?

• To check the solution

• To simplify the equation further

• To isolate the variable term by undoing subtraction

• To eliminate the variable

What operation is performed to solve for the variable after isolating the term 8W?

• Multiply both sides by 8

• Subtract 8 from both sides

• Divide both sides by 8

• Add 8 to both sides

What is the final solution for W in the equation?

• W = -8/3

• W = 8/3

• W = -3/8

• W = 3/8

Why is it important to verify the solution by substituting back into the original equation?

• To ensure the solution satisfies the equation

• To find a different solution

• To eliminate the variable

• To simplify the equation further

What should be the result when substituting the solution back into the original equation?

• The left side should be greater than the right side

• The right side should be zero

• The left side should be less than the right side

• Both sides should be equal

What is the value of the expression on both sides after substitution?

• 558

• -558

• -38

• 38

What is the significance of the solution W = -3/8?

• It is a random number

• It is the midpoint of the equation

• It satisfies the original equation

• It is the average of the terms