Solving Equations with Fractions

The video tutorial explains how to solve an equation involving fractions by first clearing the fractions using the least common denominator. It then demonstrates simplifying the equation and solving it step-by-step. Finally, the solution is verified by substituting it back into the original equation to ensure correctness.

What is the first step in solving the equation 74x + 8 = 112?

• Divide both sides by 74

• Add 8 to both sides

• Subtract 8 from both sides

• Multiply both sides by 74

Why is it beneficial to clear fractions from an equation before solving?

• It simplifies the equation

• It makes the equation more complex

• It makes the equation longer

• It adds more variables

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

• 4

• 24

• 8

• 12

After clearing fractions, what is the simplified equation?

• 74x + 8 = 112

• 42x + 3 = 2

• 42x + 8 = 3

• 24x + 8 = 112

What operation is performed to isolate the variable term 42x in the equation 42x + 3 = 2?

• Divide both sides by 42

• Multiply both sides by 42

• Subtract 3 from both sides

• Add 3 to both sides

What is the result of subtracting 3 from both sides of the equation 42x + 3 = 2?

• 42x = 3

• 42x = 2

• 42x = -1

• 42x = 5

What is the final step to solve for x in the equation 42x = -1?

• Multiply both sides by 42

• Divide both sides by 42

• Add 1 to both sides

• Subtract 1 from both sides

What is the solution for x in the equation 42x = -1?

• x = -42

• x = -1/42

• x = 42

• x = 1/42

How do we verify the solution x = -1/42?

• By checking if x = 1/42 satisfies the equation

• By multiplying x by 42

• By solving a different equation

• By substituting x = -1/42 back into the original equation

What is the result when substituting x = -1/42 back into the original equation?

• The left side equals 1

• The left side equals 0

• The left side equals -112

• The left side equals 112