Solving Equations with Fractions

The video tutorial explains how to solve equations with variables on both sides, focusing on handling fractions. It introduces two methods: solving with fractions and eliminating fractions by multiplying by the least common multiple. The tutorial provides step-by-step guidance for each method, emphasizing the importance of understanding fractions and operations. The video concludes by affirming that both methods yield the same result, offering flexibility in approach.

What is the main goal when solving for x in an equation with variables on both sides?

• To multiply both sides by zero

• To make both sides equal zero

• To isolate x on one side

• To eliminate all variables

What is the first step in solving an equation with variables on both sides?

• Multiply both sides by zero

• Subtract the smaller variable from both sides

• Add the variables together

• Divide both sides by the variable

Why is solving equations with fractions considered challenging?

• Fractions cannot be subtracted

• Fractions require finding common denominators

• Fractions make equations longer

• Fractions are difficult to multiply

What is the first step in solving the equation 2/3 x - 16 = 12x + 56 using the first method?

• Subtract 12x from both sides

• Multiply by 6

• Subtract 2/3 x from both sides

• Add 16 to both sides

When subtracting fractions, why do we need to find a common denominator?

• To convert fractions to decimals

• To make the fractions larger

• To simplify the fractions

• To ensure the fractions can be subtracted

What operation is used to eliminate the variable on the right side in the first method?

• Multiplication

• Division

• Subtraction

• Addition

After subtracting fractions, what is the next step in the first method?

• Subtract 56 from both sides

• Add 16 to both sides

• Multiply by the reciprocal

• Divide by 16

What is the purpose of multiplying by the least common multiple in the second method?

• To divide fractions

• To make the equation longer

• To eliminate fractions

• To add fractions

What is the first step in the second method?

• Divide by 6

• Subtract 12x from both sides

• Multiply by the least common multiple

• Add 16 to both sides

What is the least common multiple of 3, 6, 2, and 6?

• 24

• 12

• 18

• 6