I need help on a word problem.?

Question

find three consecutive integers such that -5 times the sum of the first and the third is 24 greater than 4 times the opposite if the second.
please explain and how you got the answer plz.

Answer 1

The other answerers are incorrect. The formula is:
-5[x + (x + 2)] = 24 + 4(-[x + 1])

Solve:
-5(2x + 2) = 24 - 4x - 4
-10x - 10 = 20 - 4x
6x = -30
x = -30/6 = -5

The numbers are -5, -4, and -3.


Check:
-5[x + (x + 2)] = 24 + 4(-[x + 1])
-5[-5 + (-5 + 2)] = 24 + 4(-[-5 + 1])
-5(-5 - 3) = 24 + 4(5 - 1)
25 + 15 = 24 + 4(4)
40 = 24 + 16
40 = 40

Answer 2

Whenever we solve any word problem involving algebra, we must first start by defining x to be some standard of comparison. In our case, we can just let x equal the first number. That means, since we have three consecutive integers:

x = the first number
x + 1 = the second number
x + 2 = the third number.

Note what we're given:

"such that -5 times the sum of the first and third ..." translates to:

(-5)[x + (x + 2)] {x is the first number, x + 2 is the third number}

"is 24 greater than 4 times the opposite of the second."

(-5)[x + (x + 2)] + 24 = 4( - [x + 1])

Note what I did above; since it is 24 greater, then you would be putting +24 to represent that. Also, the "opposite" of a number means the opposite signwise; the opposite of 5 is -5, the opposite of -17 is 17, and the opposite of (x + 1) is -(x + 1).

Thus, this is our final equation.

(-5)[x + (x + 2)] + 24 = 4( - [x + 1])

Let's simplify first. Note that x + x + 2 can be simplified, as can -(x + 1).

(-5)[2x + 2] + 24 = 4 [-x - 1]

Now, let's expand out the bracketed terms.

-10x - 10 + 24 = -4x - 4

From here, it's simple algebra. Moving all x terms to the left hand side, and everything else to the right hand side, we have

-10x + 4x = 10 - 24 - 4. Combining like terms on the left hand side, and solving the right hand side normally,

-6x = -18

Therefore,

x = 3

Remember that we LET x be our *first* integer. Our second and third integer was obtained by x + 1 and x + 2. Thus, the second integer is 3 + 1 = 4, and the third integer is 3 + 2 = 5.

So our three consecutive integers are 3, 4, and 5.

Answer 3

Let x be the first number so that x+1 is the second and x+2 the third.

-5(x + x+2) = 24 + 4[-(x+2)] here I hope that the "opposite" means the negative to get
-10x - 20 = 24 -4x-8
-6x = 20 + 24 -8 = 36
x = -6
x+1 = -5
x+2 = -4

Answer 4

first make a key: 1st #=x, 2nd #=x+1, 3rd #=x+2
next, plug it into the equation: -5[x+(x+2)]=24+ x-1
simplified, it equals:-10x-10=23+x
simplified again:-10x=33+x
again:-11x=33
again:x=-3, so x+1=-2, and x+2=-1