Solving Linear Equations and Verification

The video tutorial explains how to solve a linear equation in one variable. It begins by simplifying both sides of the equation, focusing on distributing fractions and combining like terms. The process continues with isolating the variable term by adding or subtracting terms on both sides. Finally, the solution is found by dividing, and the correctness of the solution is verified by substituting back into the original equation.

What is the first step in solving a linear equation?

• Add a constant to both sides

• Simplify both sides by eliminating parentheses and combining like terms

• Subtract a variable from both sides

• Multiply both sides by a constant

When distributing a fraction, what should you do first?

• Convert all terms to fractions

• Add the fraction to both sides

• Multiply the fraction by the constant

• Simplify common factors before multiplying

What is the common factor used to simplify 9 and 3 in the equation?

• 3

• 2

• 4

• 1

What is the simplified form of 2/3 * 9x?

• 3x

• 12x

• 6x

• 9x

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

• Add a constant to both sides

• Add or subtract terms to collect variable terms on one side

• Multiply both sides by the variable

• Divide both sides by a constant

What operation is used to solve for the variable after isolating it?

• Division

• Multiplication

• Subtraction

• Addition

What is the solution to the equation 4X = 16?

• X = 16

• X = 4

• X = 8

• X = 2

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

• To simplify the equation further

• To eliminate fractions

• To find a different solution

• To ensure the solution is correct

What is the result of substituting X = 4 back into the original equation?

• The equation is not affected

• The equation is verified as true

• The equation becomes more complex

• The equation becomes false

What is the final step in verifying the solution of a linear equation?

• Multiply both sides by a constant

• Check the solution by substituting back into the original equation

• Add a constant to both sides

• Subtract a variable from both sides