Solving Linear Equations in One Variable

The video tutorial explains how to solve a linear equation in one variable by isolating the variable on one side. It begins by addressing the presence of fractions and demonstrates how to clear them using the least common multiple. The tutorial then covers distributing terms and combining like terms to simplify the equation. Finally, it shows how to isolate the variable and verify the solution.

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

• To add fractions to both sides

• To multiply both sides by zero

• To isolate the variable on one side of the equation

• To eliminate all numbers from the equation

What is the first step in solving an equation with fractions?

• Add the fractions together

• Divide both sides by the largest fraction

• Clear the fractions by finding the least common denominator

• Subtract the fractions from both sides

What is the least common multiple of 6 and 4?

• 8

• 10

• 24

• 12

Why might you choose to multiply by the least common multiple instead of the product of the denominators?

• To make the equation unsolvable

• To increase the number of fractions

• To make the equation more complex

• To avoid additional simplifying later

After clearing fractions, what is the next step in solving the equation?

• Multiply by another number

• Clear the parentheses by distributing terms

• Add more fractions

• Divide by the variable

What does combining like terms help achieve in an equation?

• It makes the equation longer

• It helps isolate the variable

• It adds more variables

• It makes the equation unsolvable

What operation is used to move variable terms to one side of the equation?

• Addition

• Subtraction

• Multiplication

• Division

What is the opposite operation of subtracting 9 in an equation?

• Subtracting 9

• Dividing by 9

• Adding 9

• Multiplying by 9

What is the final value of x in the solved equation?

• 65

• 0

• -65

• 9

Why is it important to verify the solution of an equation?

• To ensure the equation is incorrect

• To add more variables

• To confirm the solution satisfies the original equation

• To make the equation more complex