Solving Linear Equations and Verification

The video tutorial explains how to solve the equation derived from the problem statement: the sum of 13 times a number and three equals 172. The variable x is used to represent the unknown number. The tutorial guides through formulating the equation 13x + 3 = 172, solving it by isolating x, and verifying the solution by substituting back into the original equation. The solution is confirmed as correct, with x equaling 13.

What is the initial problem statement in the video?

• The quotient of 13 times a number and three is 172.

• The product of 13 and a number is 172.

• The sum of 13 times a number and three is 172.

• The difference between 13 times a number and three is 172.

Which variable is used to represent the unknown number?

• x

• y

• z

• n

How is the equation derived from the problem statement?

• 13x - 3 = 172

• 13x + 3 = 172

• 13x * 3 = 172

• 13x / 3 = 172

What is the first step in solving the equation 13x + 3 = 172?

• Add 3 to both sides

• Multiply both sides by 13

• Subtract 3 from both sides

• Divide both sides by 13

After subtracting 3 from both sides, what does the equation become?

• 13x = 169

• 13x = 175

• 13x = 172

• 13x = 165

What operation is performed to isolate x in the equation 13x = 169?

• Add 13 to both sides

• Divide both sides by 13

• Subtract 13 from both sides

• Multiply both sides by 13

What is the value of x after solving the equation?

• 12

• 13

• 14

• 15

How do you verify the solution to the equation?

• By checking if 13 times the number plus 3 equals 172

• By checking if 13 times the number minus 3 equals 172

• By checking if 13 times the number divided by 3 equals 172

• By checking if 13 times the number multiplied by 3 equals 172

What is the result of 13 times 13 plus 3?

• 169

• 178

• 172

• 175

What does the verification step confirm about the solution?

• The solution is incorrect

• The solution needs adjustment

• The solution is partially correct

• The solution is correct