Atriangle has the following side lengths: x - 2, x, and 3x + 1. another triangle has the following side lengths: 2x - 5, x + 4, 6x - 7. if the perimeters of the two triangles are equal, what is x?

Since we know that the perimeters are equal, we can make an equation where the sum of the side lengths of one triangle equal the sum of the side lengths of the other triangle. This yields (x-2)+(x)+(3x+1)=(2x-5)+(x+4)+(6x-7). If we combine like turns, the equation becomes 5x-1=9x-8. We can use the subtraction property of equality to isolate the x and the integers by saying 9x-5x=-1-(-8). Simplifying this gives 4x=7 or x=1.75

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