Solving Equations with Inverse Operations

This lesson teaches how to solve equations of the form a/b * x = c using inverse operations. The goal is to isolate the variable by applying inverse operations to both sides of the equation. The lesson includes examples such as solving 7x = 14 and (1/3)x = -9, demonstrating the use of division and multiplication. It also covers combining inverse operations in multi-step equations and emphasizes verifying solutions to ensure accuracy.

What is the primary goal when solving equations using inverse operations?

• To make both sides of the equation different

• To make the equation more complex

• To find the value of the variable

• To eliminate all variables

What is the inverse operation of multiplication?

• Addition

• Exponentiation

• Subtraction

• Division

In the example '7 times x equals 14', what operation is used to isolate x?

• Divide both sides by 7

• Multiply both sides by 7

• Add 7 to both sides

• Subtract 7 from both sides

How do you eliminate division by a fraction in an equation?

• Add the fraction to both sides

• Divide both sides by the reciprocal of the fraction

• Subtract the fraction from both sides

• Multiply both sides by the reciprocal of the fraction

What is the result of multiplying both sides of the equation 'one-third x equals negative nine' by 3?

• x equals negative 3

• x equals 27

• x equals 3

• x equals negative 27

In a multi-step equation, what happens to the equation after each inverse operation?

• It becomes more complex

• It remains the same

• It becomes simpler

• It becomes unsolvable

What is the inverse operation of multiplying by two?

• Multiplying by two

• Adding two

• Subtracting two

• Dividing by two

What is the final value of x in the equation '2x equals negative 81' after applying the inverse operation?

• x equals negative 81

• x equals 81

• x equals negative 40.5

• x equals 40.5

Why is it important to verify the solution of an equation?

• To eliminate the variable

• To change the solution

• To ensure the solution is correct

• To make the equation more complex

What should the result be when substituting the solution back into the original equation?

• The variable is eliminated

• The original equation is satisfied

• An incorrect solution

• A different equation