Understanding and Solving Algebraic Equations

The video tutorial guides viewers through translating a sentence into an algebraic equation, solving for the unknown variable x, and verifying the solution. It begins with forming the equation from the problem statement, then proceeds to distribute and simplify the equation. The tutorial continues by isolating the variable x and solving the equation. Finally, it verifies the solution by substituting the value back into the original equation to ensure correctness.

What is the first step in translating a sentence into an equation?

• Check the solution with a calculator.

• Solve the equation immediately.

• Identify the variable to use.

• Multiply all terms by two.

How do you express 'three more than a number' using a variable x?

• x - 3

• 3x

• 3 - x

• x + 3

What operation is used to clear the parentheses in the equation?

• Addition

• Subtraction

• Multiplication

• Division

What is the result of distributing 6 in the expression 6(x + 3)?

• 6x + 3

• 6x - 3

• 6x + 18

• 6x - 18

What is the next step after distributing in the equation 6x + 18 = 32?

• Divide both sides by 6.

• Subtract 18 from both sides.

• Multiply both sides by 6.

• Add 18 to both sides.

What is the simplified form of the fraction 14/6?

• 7/3

• 3/7

• 6/14

• 14/3

What common factor is used to simplify the fraction 14/6?

• 3

• 4

• 2

• 5

What is the final value of x in the equation?

• 14

• 6

• 7/3

• 3

How do you verify the solution of an equation?

• By guessing the answer.

• By substituting the solution back into the original equation.

• By multiplying the solution by 2.

• By adding 10 to the solution.

What should the left side of the equation equal after substitution?

• 18

• 14

• 6

• 32