Linear Equation Solving Techniques

The video tutorial explains how to solve linear equations by isolating the variable. It presents two methods: clearing fractions by finding the least common multiple and working directly with fractions. The first method involves multiplying each term by the least common multiple to eliminate fractions, while the second method combines fractions by finding a common denominator. Both methods lead to the same solution, demonstrating flexibility in solving linear equations.

What is the primary goal when solving a linear equation?

• To eliminate all constants

• To find the least common multiple

• To isolate the variable on one side

• To multiply all terms by zero

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

• Clear the fractions by finding the least common denominator

• Add all fractions together

• Convert fractions to decimals

• Divide all terms by the largest fraction

What is the least common multiple of 5, 3, and 4?

• 15

• 30

• 60

• 120

When multiplying each term by the least common multiple, what is the result for the term 5x?

• 5x

• 12x

• 20x

• 60x

After clearing fractions, what is the equation before isolating x?

• 32x = 60

• 32x = 45

• 12x = 60

• 20x = 45

What is the solution for x after dividing both sides by 32?

• x = 45/32

• x = 0

• x = 32/45

• x = 1

What is the least common denominator for fractions with denominators 5 and 3?

• 5

• 20

• 10

• 15

What is the result of combining 3x/15 and 5x/15?

• 8x/15

• 5x/3

• 3x/5

• 15x/15

What is the reciprocal of 8/15 used to isolate x?

• 15/8

• 8/15

• 1/8

• 1/15

What is the final solution for x using both methods?

• x = 32/45

• x = 1 and 13/32

• x = 0

• x = 45/32