The larger of two consecutive integers is 13 greater than four times the smaller. find the integers

a. 3,4
b. -3,-4
c. 7,8

The integers are -3 and -4.

Let's represent

The larger consecutive integer as: x

The smaller consecutive integer as: y

Consecutive integers are represented as:

x , x + 1

where,

x = x + 1

y = x

The larger of two consecutive integers is 13 greater than four times the smaller. This is expressed algebraically as:

x = 4y + 13

Substitute x + 1 for x and x for y in Equation 1

x + 1 = 4x + 13

Collect like terms

 x - 4x = 13 - 1

-3x = 12

Divide both sides by -3

-3x/-3 = 12 /-3

x = -4

Therefore, the smaller integer is -4

Solving for x

x + 1

-4 + 1  

= -3

Therefore, the larger integer is -3

The correct option is Option B

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now, let's keep in mind that, the integers are consecutrive, therefore, if one is say 2, the other is either, 3 or 1, because 1,2,3  <--- notice, 1 is before 2 and 3 is after 2.

so say, our first integer is "a", then the next one can just be "a+1".

let's recall that, on the negative side in a number line, the closer to 0, the larger the number, therefore, -1,000,000 is a much smaller number than -1, because -1 is closer to 0, thus is larger.

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)