Math Is Easy - Use Algebra To Solve Word Problem 9!

Find three consecutive even integers such that fourtimes the first minus the third is 6 more than twice the second. (Note1)

Since even consecutive integers differ by 2 (2,4,6), wecan represent them as follows:

let n represent the smallest of the three consecutiveintegers; then n + 2 represents the second largest and, n + 4 represents thelargest .

We can now create the following equation:

4(n) - (n + 4) =2 (n + 2) + 6

Solve this equation

4(n) - (n +4) =2(n + 2) + 6

4nn4 =2n + 4 + 6 Remove parentheses

3n - 4 = 2n + 10 Add thecommon terms

3n - 4 = 2n + 10

+ 4 = + 4 Add 4 to each side

3n + 0 = 2n + 14

3n = 2n + 14

-2n= -2n Subtract 2n from each side

1n = 0n + 14

n = 14

Now we substitute the answerfor n into the original equation to see if it works.

4(n) - (n + 4) =2 (n + 2) + 6

4(14) - (14 + 4)= 2 (14 + 2) + 6

4(14) - (18) = 2(16) + 6

56 - 18 = 32 + 6

38 = 38

We must also see if the solution works in the originalproblem statement.

Find three consecutive even integers such that fourtimes the first minus the third is 6 more than twice the second.

Find three consecutive even integers (14,16,18 areconsecutive even integers) such that four times the first (4 X 14) minus thethird (18) is 6 more than twice the second (2 X 16).

Find three consecutive even integers such that fourtimes the first (56) minus the third (18) is 6 more than twice the second(32).

Find three consecutive even integers such that 56 minus18 is 6 more than 32.

5618 = 6 + 32

38 = 38

We have just solved a first degree equation.

(Note1)

The source for the problem statement is:

Intermediate AlgebraFor College Students by Jerome E. Kaufman


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