solve the following equations 3x-5=7 and 5-2(x-1)=3x-8?

3x -5 = 7
3x = 12
x = 4


5 -2(x-1) = 3x -8
5 -2x +2 = 3x -8
7 -2x = 3x -8
15 = 5x
x = 3

1)
3x - 5 = 7
3x = 7 + 5
x = 12/3
x = 4

2)
5 - 2(x - 1) = 3x - 8
5 - 2*x + 2*1 = 3x - 8
5 - 2x + 2 = 3x - 8
-3x - 2x = -5 - 8 - 2
-5x = -15
x = -15/-5
x = 3

3x -5 = 7
add 5 to both sides
3x = 12
divide both sides by 3
x = 4


5 - 2(x - 1) = 3x - 8
break brackets first
5 - 2x + 2 = 3x - 8
7 - 2x = 3x - 8
add 2x to each side
7 = 5x - 8
add 8 to each side
15 = 5x
divide by 5
x = 3

for the first part x =4

for the second x =3

1 - first add 5 to both sides that gives you 3x = 12 divide through by 3 x = 4

2 first get rid of the bracket by multiplying the -2 into it this gives you 5-2x+2 = 3x-8

next andd 2x to both sides and 8 to both sides and you get 15= 5x then divide through by 5 to get the x=3

hope this helps

1) Notice that one equation has +y and one h as -y. If you were to ADD those two terms they would cancel. Thus, if you were to add the two equation the y's would cancel and leave you with an equation with ONLY x in it. Then you could solve for x, then use EITHER of the two equations to find y. 2) Notice that one equation has 4y and the other ALSO has 4y, so just SUBTRACT the two equations and the y's will cancel (you could have done this with the 1st equation since x and x were in common) 3) look at 2x and -4x, ALL you have to do is multiply the 2x by 2 and then add them so that they cancel: So multiply top equation by 2: 2 * (2x + 5y = 13) --> 4x + 10y = 26 Now you have: 4x + 10y = 26 -4x - 3y = 9 <-- second equation remains UNCHANGED Now just ADD to cancel out the x's, solve for y, then you can get x from either of these original two (by using y). 4) This is the general case. You are doing this case in the above three but with some simplifications. Here there is no "easy" way to get either x's OR the y's to cancel. But the solution IS easy: you have 3x and 4x: Find a number they have in common then multiply to get that number (i.e. 12: 3 * 4 = 12 and 4 * 3 = 12). 12 is an arbitrary choice, you can multiply to make them the same number in INFINITELY different ways: for example, if you are not afraid of fractions then we can make BOTH x's have a coefficient of one: (1/4) * (4x + 7y = 1) --> x + (7/4) * y = (1/4) (1/3) * (3x + 2y = -9) --> x + (2/3) * y = -3 Now solve these equations: x + (7/4)y = (1/4) x + (2/3)y = -3 by subtracting: ((7/4) - (2/3)) * y = (1/4) - (-3) = 3 + 1/4 7/4 - 2/3 = 21/12 - 8/12 = 13/12 3 + 1/4 = 13/4 so you have: (13/12) * y = 13/4 --> y = (13/4) * (12/13) = 12/4 = 3 (to get rid of the multiply by (13/12) you multiply by it's reciprocal: (12/13), thus this is where the * (12/13) is coming from on the right, (I don't show anything on the left because I know the purpose of multiplying by 12/13 was to get y by itself, really meaning it has a coefficient of 1) x + (7/4)y = 1/4 --> x + (7/4) * 3 = 1/4 --> x = (1/4) - 21/4 = -20/4 = -5 so x = -5, y = 3 Now, obviously, this was nasty because of the fractions. ALL of that could have been avoid by making the x's by 12x instead of 1x...but I think it's instructional that you get the same ANSWER either way. Here's the same problem done MUCH quicker: 4x + 7y = 1 --> (*3) --> 12x + 21y = 3 3x + 2y = -9 --> (*4) --> 12x + 8y = -36 subtracting: 13y = 3 - (-36) = 36 + 3 = 39 --> y = 39/13 = 3 4x + 7 * (3) = 1 --> 4x = 1 - 21 = -20 --> x = -20/4 = -5 (so again, x = -5, y = 3) Hopefully from this last one you can solve the easier 1), 2), and 3) problems.

3 x = 12
x = 4


5 - 2 x + 2 = 3 x - 8
15 = = 5 x
x = 3

i agree witht he person above

Are you serious? I could do this when I was in 5th grade. You are never going to learn when you get other people to do it for you. Then again, you probably like Miley Cirus and the Jonas Brothers so I don't reckon there is much point in trying to talk sense into you. Thanks for ruining the future of America