Understanding Algebraic Equations

The video tutorial explains how to solve a math problem where one number is 14 more than four times another, and their sum is 114. It begins by defining variables and formulating expressions, then sets up an equation to solve for x. The solution involves combining like terms, isolating the variable, and performing arithmetic operations to find the values of the numbers. The tutorial concludes by verifying the solution and summarizing the steps taken.

What is the relationship between the two numbers described in the problem?

• One number is 14 less than four times another.

• One number is 14 times another.

• One number is four times another.

• One number is 14 more than four times another.

If x represents a number, how would you express 14 more than four times x?

• x + 14

• 4x + 14

• 14x + 4

• 4x - 14

What equation represents the sum of the two numbers being 114?

• x + 4x = 114

• x + (4x + 14) = 114

• 4x + 14 = 114

• x + 14 = 114

What is the first step in solving the equation x + (4x + 14) = 114?

• Subtract 14 from both sides.

• Add 14 to both sides.

• Combine like terms.

• Divide both sides by 5.

After combining like terms, what does the equation become?

• x + 14 = 114

• 4x + 14 = 114

• 5x = 114

• 5x + 14 = 114

What operation is used to isolate the variable term in the equation 5x + 14 = 114?

• Addition

• Subtraction

• Multiplication

• Division

What is the value of x after solving the equation 5x = 100?

• 15

• 10

• 25

• 20

How do you find the second number once x is known?

• Multiply x by 4 and add 14.

• Multiply x by 4 and subtract 14.

• Add 14 to x.

• Subtract 14 from x.

What is the second number if x is 20?

• 104

• 74

• 84

• 94

What is the sum of the two numbers found in the problem?

• 104

• 114

• 124

• 134