Isolating Variables in Equations

This tutorial explains how to rearrange equations to isolate specific terms, often unknowns, by reversing mathematical operations. It covers examples of isolating terms using addition, subtraction, multiplication, and division. The tutorial also demonstrates handling multiple operations in equations and applies these techniques to chemical equations, such as calculating concentration from moles and volume.

What is the first step to isolate a term in an equation like a + b = c?

• Divide both sides by b

• Multiply both sides by b

• Subtract b from both sides

• Add b to both sides

In the equation a + b = c, what happens when you subtract b from both sides?

• a is isolated

• b is isolated

• c is isolated

• The equation becomes a + b = c - b

When isolating a term in an equation using multiplication, what operation should be used?

• Subtraction

• Division

• Addition

• Multiplication

In the equation a * b = c, what operation would you perform to isolate a?

• Add b to both sides

• Subtract b from both sides

• Multiply both sides by b

• Divide both sides by b

What operation is used to cancel out a multiplication in an equation?

• Multiplication

• Addition

• Subtraction

• Division

What is the result of dividing both sides of the equation a * b = c by b?

• a = c + b

• a = b / c

• a = c / b

• a = c * b

How do you handle an equation with multiple operations, such as a * b + c = d?

• Isolate a by subtracting c and dividing by b

• Isolate a by adding c to both sides

• Isolate a by multiplying by b and adding c

• Isolate a by dividing by c and subtracting b

What is the first step to isolate a in the equation a * b + c = d?

• Add c to both sides

• Subtract c from both sides

• Multiply both sides by b

• Divide both sides by b

In the context of chemical equations, what does the expression n = c * v represent?

• Volume equals concentration times number of moles

• Number of moles equals concentration times volume

• Concentration equals number of moles times volume

• Number of moles equals volume times concentration

How would you isolate concentration (c) in the equation n = c * v?

• Multiply both sides by v

• Divide both sides by v

• Subtract v from both sides

• Add v to both sides