Solving Proportions and Verifying Solutions

The video tutorial demonstrates how to solve a proportion by using cross products. It begins with an introduction to the concept of proportions and the method of cross-multiplication. The instructor sets up the equation, explaining the importance of parentheses when dealing with binomials. The solution process involves distributing terms and simplifying the equation to find the value of x. Finally, the solution is verified by substituting back into the original proportion to ensure both sides are equal, confirming the correctness of the solution.

What is the first step suggested in the video to solve the given proportion?

• Cross-multiply the terms.

• Use a calculator to find the answer.

• Pause the video and try solving it yourself.

• Directly solve for x.

What property of proportions is used to solve them?

• Cross-multiplication.

• Subtraction of terms.

• Addition of fractions.

• Division of constants.

When using cross-multiplication, what should you be careful about?

• Only multiplying the numerators.

• Using parentheses for binomials.

• Not using parentheses for binomials.

• Ignoring the constants.

What is the result of distributing 18 across (x + 4)?

• 18 + 4x

• 18x + 72

• 18x + 4

• 18x + 18

What is the purpose of using parentheses in the expression (x + 4)?

• To add the terms.

• To divide the terms.

• To ensure correct distribution.

• To subtract the terms.

How do you isolate the variable x in the equation 18x + 72 = 12x + 84?

• Add 12x to both sides.

• Subtract 12x from both sides.

• Divide both sides by 6.

• Multiply both sides by 2.

What is the value of x after solving the equation?

• x = 2

• x = 3

• x = 4

• x = 1

What operation is performed after distributing the terms in the equation?

• Subtraction of terms.

• Multiplication of variables.

• Division of coefficients.

• Addition of constants.

What is the result of subtracting 72 from both sides of the equation?

• 6x = 84

• 6x = 12

• 18x = 84

• 12x = 72

How do you verify the solution of a proportion?

• By guessing the value of x.

• By solving another equation.

• By using a calculator.

• By checking if both sides are equal after substituting the value of x.