Consecutive Integers and Equations

This video tutorial reviews applications of linear equations, focusing on consecutive integer problems. It outlines a six-step procedure for solving word problems involving linear equations in one variable. The tutorial provides examples of solving problems with consecutive integers, even integers, multiples of seven, and odd integers, emphasizing the importance of setting up equations and verifying solutions.

What is the first step in solving a word problem involving linear equations?

• Read the problem and determine the question

• Write an equation based on the situation

• Check the answer using the words of the problem

• Assign a variable to the unknown

In the book pages problem, if the sum of two consecutive pages is 663, what is the equation to find the page numbers?

• X + X + 2 = 663

• X + 2 = 663

• X + X + 1 = 663

• X + 1 = 663

What are the page numbers if the sum of two consecutive pages is 663?

• 333 and 334

• 330 and 331

• 331 and 332

• 332 and 333

How do you represent the smallest of three consecutive even integers?

• X + 6

• X

• X + 4

• X + 2

If the sum of three consecutive even integers is 30, what is the equation to solve for the integers?

• X + X + 3 + X + 5 = 30

• X + X + 1 + X + 3 = 30

• X + X + 2 + X + 4 = 30

• X + X + 4 + X + 6 = 30

What are the three consecutive even integers whose sum is 30?

• 6, 8, 10

• 12, 14, 16

• 8, 10, 12

• 10, 12, 14

How do you represent the first of five consecutive multiples of seven?

• X + 21

• X

• X + 14

• X + 7

If the sum of five consecutive multiples of seven is 245, what is the equation to solve for the multiples?

• X + X + 5 + X + 10 + X + 15 + X + 20 = 245

• X + X + 7 + X + 14 + X + 21 + X + 28 = 245

• X + X + 6 + X + 12 + X + 18 + X + 24 = 245

• X + X + 8 + X + 16 + X + 24 + X + 32 = 245

What are the five consecutive multiples of seven whose sum is 245?

• 28, 35, 42, 49, 56

• 35, 42, 49, 56, 63

• 49, 56, 63, 70, 77

• 42, 49, 56, 63, 70

In the complex odd integers problem, how do you represent the smallest integer?

• X

• X + 4

• X + 2

• X + 6