Equations with Integer Solutions- 4m-7=2m-1?

Question

I know, it's not a very difficult one. But there's one part that's got me in a cookie. This is what I've got so far::

4m-7=2m-1
4m-7+7=2m-1+7
4m=2m-8

I think that's right. Correct me if I'm wrong. I think you subtract 2m from 4m, but then what happens to the minus sign?
Note: none of the above is actually integers, yet...Any halp appreciated, thanks.

Isn't 1+7, like....8? I'm not getting any of this :S

..But it's not -1, it's 1, isn't it? Because if you had 2m -1, it doesn't really say what to do with 1, no?

How do you know if it's negative one, or minus one though?

Answer 1

4m = 2m -1 + 7
4m = 2m + 6
-2m= -2m

2m = 6

m = 3

Answer 2

You were on the right track but you have to think about adding postivie and negative numbers

-1+7 does not equal 8 (you thought something looked wrong and you were correct, that means you have good math instincs.

-1+7 is the same as +7-1, and 7-1=6, right?

so, correcting the last step and then heading on with the subtracting of the 2m's like you planned

4m-2m=2m-2m+6
2m=6

then we divide both sides by 2

2m/2=6/2
m=3

lets check by sticking 3 in for each "m" in the original equation

4(3)-7=2(3)-1
12-7=6-1
5=5

woohoo

Answer 3

4m-7=2m-1

4m-7+7=2m-1+7

Adding the -1+7 equals 6.

4m=2m+6

2m=6

m=3

Answer 4

4m - 7 = 2m - 1 (+ 7)
4m = 2m + 6 (-2m)
2m = 6 ( / 2 )
m = 3

Answer 5

you are correct about subtracting 2m from 4m, but check your step when you added 7 to both sides. look carefully at the right hand side and see what you can find....
it's step 2 in your work

Answer 6

rule to solve all eq'ns like the one above: Gets Xs on one side and numbers on other side.

first -1+7=6 not -8
4m-2m=2m-2m + 6
2m =6
m =3

Answer 7

4m - 7 = 2m - 1
subtract 2m
2m - 7 = - 1
add 7
2m = 6
m = 3

Answer 8

x^y - y^x = x + y i desperate to ignore approximately your interest in integer strategies and map all strategies. I did this with the aid of getting a graph drawing web site to remedy the equation x^y - y^x - x - y = 0 for particular values of y. interior the 1st quadrant, area of the the answer varieties a U-formed curve which starts off with very great y values to the main stunning of x = a million, drops to a minimum at approximately (3.114, 3.647) and then curves up returned and quickly (as quickly as you pass x = 4) turns into asymptotic to the line y = x yet in basic terms above it. this suggests that there could be no integer answer with x > 2. there is yet another upside-down U-formed curve which fits left from (a million, 0) as much as a optimal at approximately (0, 5, 0.one 0 five) and then turns down in direction of the beginning place. To the main stunning of (a million, 0) it curves all the way down to alter into asymptotic to the line y = -x yet in basic terms above it. There seems to be no answer for -a million < x < 0. we are in a position to instruct theoretically that there are actually not any strategies with the restrict y = x. If this have been allowed you get x^x - x^x = 2x ----> x = 0 yet it relatively isn't allowed via fact 0^0 is undefined. If y = -x is investigated you get x^(-x) - (-x)^x = 0 ----> a million/(x^x) = (-x)^x ----> a million = (x^x)*((-x)^x) = (-x^2)^x without real answer. as a result the aspects of the curve can not circulate the two strains y = x and y = -x. unusual issues ensue in case you attempt utilising unfavorable values for x or y. There seems to be yet another area of the curve (or in line with hazard 2 extra disjoint aspects) for this equation that's asymptotic to y = -x. The maximum unearthly element occurs in case you put in y = a million.8, a million.9, 2, 2.a million, 2.2 and remedy for x. You get -2.a million, -2.2, -a million.2, -2.3, -2.4 that's confusing to describe.

Answer 9

4m-7=2m-1
4m-2m=-1+7
2m=6
m=6/2
m=3

Answer 10

4m=2m-1+7
4m=2m+6
4m-2m=2m+6-2m
2m=6
m=3