Solving Linear Equations and Verification

The video tutorial explains how to solve a linear equation in one variable, both with and without clearing fractions. It demonstrates the process of isolating the variable, using reciprocal multiplication, and verifying the solution by substitution. The tutorial emphasizes understanding each step to ensure the solution is correct.

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

• To find the least common multiple of the coefficients

• To eliminate all variables from the equation

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

• To convert the equation into a quadratic equation

What is the first step in solving the equation 4/5 X + 2 = -6?

• Subtract 2 from both sides

• Divide both sides by 4

• Multiply both sides by 4/5

• Add 2 to both sides

After isolating the variable term 4/5 X, what is the next step?

• Subtract 4/5 from both sides

• Add 4/5 to both sides

• Divide both sides by 5/4

• Multiply both sides by 5/4

What is the solution to the equation 4/5 X + 2 = -6?

• X = -10

• X = 10

• X = -8

• X = 8

What is the least common denominator used to clear the fraction in the equation?

• 5

• 4

• 1

• 10

What operation is performed after clearing the fraction to isolate 4X?

• Divide both sides by 4

• Multiply both sides by 4

• Subtract 10 from both sides

• Add 10 to both sides

What is the final solution after solving the equation by clearing the fraction?

• X = -8

• X = 10

• X = 8

• X = -10

How do you verify the solution to the equation?

• By ensuring the solution is an integer

• By substituting the solution back into the original equation

• By solving the equation again using a different method

• By checking if the solution is a positive number

What is the result of substituting X = -10 back into the original equation?

• The left side equals -6

• The left side equals -8

• The left side equals 0

• The left side equals -10

What does the verification step confirm about the solution?

• The solution is a positive number

• The solution needs to be adjusted

• The solution satisfies the original equation

• The solution is incorrect