solve this problem please?

Question

(1)what are the two consecutive integers such that twice the smaller decreased by the larger equal -59?

(2)There are four consecutive odd integers. the sum of the first and third # is 142. what are the integers?

Answer 1

1) let the two integers be x and x+1
then set up the equation...
2x - (x +1) = -59
solve for x
you get ... x= -58
then plug it back in... x +1= -58 +1 = -57
thus your two numbers are -58 and -57

2) name 4 integers by using variables.
the easiest way would be to call them (first odd number) x, (second odd number) x+2, (third odd number) x+4, (fourth odd number) x+6
(you keep adding two because you want odd numbers, if you add 1 you will get even numbers as well)
then do what the words tell you and find the equation
the equation is x + (x+4) = 142
solve for x again... 2x = 142 -4
x = 69
then plug x back in for each value.
69, 71, 73, 75

Answer 2

Part 1:
2 consecutive integers are two numbers next to each other such as 1 and 2.

So you let x = smaller number
x+1 = larger number

Twice the smaller decreased by the larger is equal to -59 is:

2x - (x+1) = -59 --> Don't forget to switch signs
2x - x - 1 = -59
2x - x = -59+1
x = -58
x+1 = -57

Now test the answers:
2(-58)- (-57) = -59
-59 = -59 --> It's right!

Part 2:
Four consecutive odd integers are four numbers that are odd, right after another such as (3, 5, 7, 9)
First number = x
Second number = x + 2
Third number = x+4
Fourth number = x+6

The sum of the first and third is 142:
x + x +4 = 142
2x = 142-4
2x = 138
2x/2 = 138/2
x = 69
x+4 = 73

Test:
69 +73 = 142

It's right!
-114+58 = -59

Answer 3

1.) integer 1 = x
integer 2 = x + 1

2(x) - (x + 1) = -59
2x - x - 1 = -59
x - 1 = -59
x = -58

integer 1 = -58
integer 2 = -57


2.) integer 1 = 2x + 1
integer 2 = 2x + 3
integer 3 = 2x + 5
integer 4 = 2x + 7

* To make sure that a number is odd, first make it even (by multiplying by 2) and then add 1. Try it. No matter what number you start with - even or odd - multiplying it by 2 and adding 1 will make sure it's odd.

(2x + 1) + (2x + 5) = 142
4x + 6 = 142
4x = 136
x = 34

integer 1 = 2(34) + 1 = 69
integer 2 = 2(34) + 3 = 71
integer 3 = 2(34) + 5 = 73
integer 4 = 2(34) + 7 = 75

Answer 4

(1)

ok
2x - y= -59

y - x= 1 or y =1 - x

substitute y

2x- (1 - x)= -59
2x -1 + x = -59 combine like terms
3x = -60
x= -20
y= -19


(2)

so 142 / 2 = 71, subtract two from 71, add two to 71

69+73= 142

so the numbers are 69 71 73 75

Answer 5

1) 2x-(x+1)= -59
2x-x-1= -59
x-1= -59
x= -58
-58,-57

2) x+x+4=142
2x+4=142
2x=138
x=69
69,71,73,75

Answer 6

1) x= -60
x+1= -59

2) x=70
x+1=71
x+2=72
x+3=73

Answer 7

(1) -58, -57

(2) 69, 71, 73, 75

I'm pretty sure about these. Check them out.

Answer 8

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