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# 13x-3=4x-4

but the answer has to be x=1 or 3 or -1 or-2

There's really only one way to solve this:

13x - 3 = 4x - 4

13x - 4x - 3 = 4x - 4x -4  (subtract 4x from both sides to get all x's on the same side)

9x -3 = -4

9x -3 +3 = -4 +3   (add 3 to both sides, to get x's alone)

9x = -1

9x/9 = -1/9  (divide both sides by 9, to get x alone)

x = -1/9  (minus one ninth)

Let's prove it, by making x in the original equation = -1/9:

(13)(-1//9) -3 = (4)(-1/9) - 4

-13/9 - 3  = -4/9 - 4

-13/9 + 4/9 = -4 + 3

-9/9 -1; -1 = -1   (proven - it works!)

If we try x=1, or x=3, or x=-1, or x=-2, it won't work (both sides of the equation will not be equal)

Let's try one of them, x=1, then you can try the other 3:

(13)(1) - 3 = (4)(1) - 4

13-3 = 4-4; or 10 = 0  (NOT!  won't work; 10 does not equal zero)

13x - 3 = 4x - 4                  Given

13x - 3 + 3 = 4x - 4 + 3      Add 3 to each side

13x + 0 = 4x - 4 + 3           Inverse property of addition

13x = 4x - 4 + 3                 Identity property of addition

13x = 4x - 1                       Simplify (-4 + 3 = -1)

13x - 4x = 4x - 4x - 1          Subtract 4 from each side

13x - 4x = 0 - 1                  Inverse property of addition

13x - 4x = -1                      Identity property of addition

9x = -1                              Simplify (13x - 4x = 9x)

9x/9 = -1/9                       Divide each side by 9

x = -1/9                            Inverse property of multiplication

The answer cannot be any of the 4 that you have given.