Solving Linear Equations and Fractions

The video tutorial explains how to solve a linear equation in one variable. It demonstrates two methods: solving directly and solving by clearing fractions. The tutorial verifies the solution by substituting the value back into the original equation, ensuring the solution is correct.

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

• To find the least common denominator

• To rewrite the equation in a different form

• To eliminate all fractions from the equation

• To find the value of the variable that satisfies the equation

What is the first step in solving the equation 2/3x - 3 = 12?

• Subtract 12 from both sides

• Multiply both sides by 3

• Add 3 to both sides

• Divide both sides by 2/3

How do you isolate the variable x in the equation 2/3x = 15?

• Subtract 15 from both sides

• Multiply both sides by 3/2

• Divide both sides by 15

• Multiply both sides by 2/3

What operation is equivalent to dividing by a fraction?

• Dividing by the reciprocal

• Adding the reciprocal

• Multiplying by the reciprocal

• Subtracting the reciprocal

What is the least common denominator used to clear fractions in the equation 2/3x - 3 = 12?

• 2

• 3

• 6

• 12

After clearing fractions, what is the resulting equation from 2/3x - 3 = 12?

• 2x - 3 = 12

• 2x - 9 = 36

• 3x - 3 = 12

• 3x - 9 = 36

What is the final step to solve 2x = 45 after clearing fractions?

• Subtract 45 from both sides

• Add 45 to both sides

• Divide both sides by 2

• Multiply both sides by 2

What is the solution to the equation 2/3x - 3 = 12?

• x = 30

• x = 45

• x = 60

• x = 15

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

• To check for calculation errors

• To simplify the equation further

• To find alternative solutions

• To ensure the solution satisfies the original equation

What is the result of substituting x = 45 back into the original equation 2/3x - 3 = 12?

• 15 - 3 = 12

• 12 - 3 = 9

• 45 - 3 = 42

• 30 - 3 = 27