Understanding Deductive Reasoning in Solving Equations

The video tutorial explains how Hiram solved the equation 5 + √(x + 14) = x + 7 using logical steps. It covers subtracting, squaring, expanding, and factoring to find solutions. The zero product property is used to determine possible values of x, which are then verified by substitution. The tutorial emphasizes deductive reasoning, starting from known facts and using logical operations to deduce new truths. It also discusses why one solution is invalid due to the principal square root.

What is the first step Hiram takes to solve the equation?

• He subtracts 5 from both sides.

• He multiplies both sides by 2.

• He adds 5 to both sides.

• He divides both sides by 5.

After squaring both sides, what does Hiram do next?

• He expands the squared binomial.

• He adds 14 to both sides.

• He divides by 2.

• He subtracts x from both sides.

What is the result of expanding (x + 2) squared?

• x^2 + 4x + 2

• x^2 + 2x + 4

• x^2 + 4x + 4

• x^2 + 2x + 2

How does Hiram factor the quadratic equation?

• By finding two numbers that multiply to 10 and add to 3.

• By finding two numbers that multiply to 3 and add to -10.

• By finding two numbers that multiply to 3 and add to 10.

• By finding two numbers that multiply to -10 and add to 3.

What property does Hiram use to solve the factored equation?

• Commutative Property

• Zero Product Property

• Associative Property

• Distributive Property

Why is x = -5 not a valid solution?

• Because it does not satisfy the original equation.

• Because it makes the equation undefined.

• Because it is not a real number.

• Because it results in a negative square root.

What is the correct solution for the equation?

• x = -5

• x = 5

• x = 2

• x = 0

What type of reasoning does Hiram use to solve the equation?

• Deductive reasoning

• Analogical reasoning

• Inductive reasoning

• Abductive reasoning

What does deductive reasoning involve?

• Starting with a hypothesis and testing it through experiments.

• Starting with known facts and using logical steps to reach a conclusion.

• Starting with specific observations and forming a general conclusion.

• Starting with assumptions and making predictions.

Why is deductive reasoning important in solving equations?

• It ensures that conclusions are based on logical steps from known facts.

• It helps in identifying patterns and trends.

• It allows for creative and innovative solutions.

• It allows for estimation and approximation.