algebra help??? (ugh ik)?

okay so like theres a way to solve this but idk how...

and example issss....

twice the greater of 2 consecutive odd intergers is 13 less thanthree times the lesser. Find the intergers.

my teacher said it was something liikkeee.e...

x and x+2,,, then u have to do somehitng else???

if u can, can u please show me using the example above!!

thanks!!!

Update:

waiiittt no.,.. can u please use the example...

twice a number increased by 12 is equal to 31 less than 3 times the number. Find the intergers.

thanks, this one hurts my brain justthinking about it

Update 2:

okay thanks people! can u tell me if im doing it right with this one?

8 minus 2 times a number is equal to the number plus 17.

8-2n=n+17 (right?)

8-2n=n+17

+8 +8 (8s cancel here?)

-2n=n+25

-2n -2n (-2ns cancel here)

leaving wiht... -2+25???

which is... n=23????

sorry u gotta talk like kindergarten with math for me

Update 3:

wait the ns dont cancel out do they?

5 Answers

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  • 1 decade ago
    Favorite Answer

    twice a number increased by 12 [ 2x + 12 ] is equal to [ = ] 31 less than 3 times the number [ 3x - 31 ].

    Write the equation:

    2x + 12 = 3x - 31

    add 31 to both sides

    2x + 43 = 3x

    subtract 2x from both sides

    43 = x, or x = 43

    Using your first example:

    twice the greater of 2 consecutive odd integers [ 2(x + 2)] is [=] 13 less than three times the lesser [ 3x - 13 ].

    Write the equation:

    2(x + 2) = 3x - 13

    Distribute the 2:

    2x + 4= 3x - 13

    Add 13 to both sides:

    2x + 17 = 3x

    Subtract 2x from both sides:

    17 = x

    So.., x (the lesser integer) is 17, and 'x + 2 ( the greater consecutive integer) is 19.

  • 1 decade ago

    Here is the first one:

    Let x be the lesser integer. Then x + 2 is the next greater consecutive odd integer, and the relationship between the numbers can be expressed this way mathematically:

    *** 2 (x + 2) = 3x - 13.

    Solving for x, we get this:

    2 (x + 2) = 3x - 13

    2x + 4 = 3x - 13

    4 + 13 = 3x - 2x

    17 = x

    x + 2 = 19

    The numbers are 17 and 19. To prove they are correct, plug them into the starred equation above to see if they produce a valid result. If they do, the equation will balance:

    2 (x + 2) = 3x - 13

    2 (19) = 3 (17) - 13

    38 = 51 - 13

    38 = 38.

    The equation balances, so x = 17 is the first odd integer, and x + 2 = 19 is the second odd integer.

    Here's the second problem:

    Let x be the number. Then *** 2x + 12 = 3x - 31. Solving for x, we get this:

    2x + 12 = 3x - 31

    12 + 31 = 3x - 2x

    43 = x

    To prove this answer is correct, plug x = 43 into the starred equation for this problem. Again, if the solution is correct, a balanced equation results:

    2x + 12 = 3x - 31

    2 (43) + 12 = 3 (43) - 31

    86 + 12 = 129 - 31

    98 = 98.

    This equation also balances, so the answer is x = 43.

    For your last problem, you set up the equation correctly, but your steps for finding n contain sign errors. Make sure you make sign changes correctly when you move pure numbers and numbers containing variables from one side of the equation to the other. Also, after you find the number you think will work, make sure you plug it into your oriignal equation to see if it actually does work. Follow the steps here:

    8 - 2n = n + 17

    Combine numbers containing n on one side of the equal side. Here we will move them to the right side:

    8 - 2n + 2n = n + 2n + 17

    8 = 3n + 17.

    Now move all pure numbers to the opposite side of the equal sign and add them:

    8 - 17 = 3n

    -9 = 3n

    Now solve for n by dividing both sides of the equation by 3:

    -9 = 3n

    -9/3 = n

    -3 = n.

    Now, show that this number works in your original equation:

    8 - 2n = n + 17

    8 - 2 (-3) = -3 + 17

    Remember, a negative number times a negative number is a positive number. So (-2) ∙ (-3) = + 6.

    8 + 6 = -3 + 17

    14 = 14.

    The equation above balances, so n = -3.

  • 1 decade ago

    2x+12=3x-31

    -2x -2x

    12=x-31

    +31 +31

    43=x

    plug in x

    2(43)+12=96

    3(43)-31=98

  • 1 decade ago

    2n+12=3n-31 thats how its set up.

    -2n -2n

    12=n-31

    +31 +31

    43=n

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  • 1 decade ago

    let x = a number

    2x+12=3x-31

    2x=3x-31-12

    2x-3x=43

    -x=43

    x = -43

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