Solving Linear Equations and Fractions

The video tutorial explains how to solve linear equations by isolating the variable. It demonstrates two examples: solving 5/3x = -30 and -9/2x = 15/28. The process involves using multiplication by the reciprocal to simplify and isolate the variable, ensuring the equation is in the form x = some number or fraction. The tutorial also covers simplification techniques, including prime factorization, to achieve the final solution.

What is the primary goal when solving a linear equation?

• To balance both sides of the equation

• To find the value of the constant

• To isolate the variable on one side

• To eliminate all fractions

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

• Addition

• Subtraction

• Multiplication by the reciprocal

• Division by the original fraction

Why do we multiply by the reciprocal instead of dividing by a fraction?

• It avoids complex numbers

• It is easier to calculate

• It is a standard mathematical rule

• It simplifies the equation more effectively

What is the simplified value of x in the first example?

• x = -18

• x = 6

• x = 18

• x = -6

In the second example, what is the reciprocal of -9/2?

• -9/2

• 2/9

• -2/9

• 9/2

What is the first step in solving the second example equation?

• Add 15/28 to both sides

• Multiply both sides by -2/9

• Subtract 9/2 from both sides

• Divide both sides by 15/28

What is the prime factorization of 28 used in the second example?

• 3 x 9

• 2 x 2 x 7

• 4 x 7

• 2 x 14

How does the sign of the product change when multiplying a negative fraction by a positive fraction?

• The product is always positive

• The product is always negative

• The product depends on the larger fraction

• The product is zero

What is the denominator of the simplified fraction in the second example?

• 21

• 42

• 14

• 28

What is the final simplified form of the second example equation?

• x = 5/28

• x = -5/42

• x = 5/42

• x = -5/28