Solving Equations with Fractions

The video tutorial explains how to solve the equation 4x = 8/7 using two methods. The first method involves using reciprocals to isolate x, while the second method clears fractions by multiplying both sides by the least common denominator. Both methods yield the same solution, x = 2/7. The solution is verified by substituting back into the original equation.

What is the main goal when solving the equation 4x = 8/7?

• To multiply both sides by 7

• To eliminate the variable x

• To convert the equation into a fraction

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

In the first method, what operation is used to isolate x?

• Adding 4 to both sides

• Multiplying both sides by 4

• Multiplying both sides by 1/4

• Subtracting 4 from both sides

What is the result of multiplying reciprocals in the equation?

• Zero

• Eight

• One

• Four

What is the solution for x in the equation 4x = 8/7 using the first method?

• x = 8/7

• x = 4/7

• x = 1/7

• x = 2/7

What is the purpose of multiplying both sides by the least common denominator in the second method?

• To add fractions

• To clear fractions from the equation

• To divide fractions

• To multiply fractions

What is the least common denominator used in the second method?

• Four

• Eight

• Seven

• Twenty-eight

After clearing fractions, what operation is performed to solve for x?

• Adding 28 to both sides

• Multiplying both sides by 28

• Dividing both sides by 28

• Subtracting 28 from both sides

What is the simplified form of the fraction 8/28?

• 8/7

• 1/7

• 4/7

• 2/7

How is the solution verified in the final step?

• By dividing both sides by 2/7

• By substituting 2/7 into the original equation

• By adding 2/7 to both sides

• By multiplying both sides by 2/7

What is the result of substituting x = 2/7 back into the original equation?

• 4/7

• 1/7

• 8/7

• 2/7