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The Rado number for the equation \\[ \\sum_{i=1}^m a_ix_i = c \\] in $r$ colours is the least positive integer $N$ such that any $r$-colouring of the integers in the interval $[1,N]$ admits a monochromatic solution to the given equation. We introduce the concept of $t$-distributability of sets of positive integers, and determine exact values whenever possible, and upper and lower bounds otherwise, for the Rado numbers when the set $\\{a_1,\\ldots,a_{m-1}\\}$ is $2$-distributable or $3$-distributable, $a_m=-1$, and $r=2$. 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The Rado number for the equation \\[ \\sum_{i=1}^m a_ix_i = c \\] in $r$ colours is the least positive integer $N$ such that any $r$-colouring of the integers in the interval $[1,N]$ admits a monochromatic solution to the given equation. We introduce the concept of $t$-distributability of sets of positive integers, and determine exact values whenever possible, and upper and lower bounds otherwise, for the Rado numbers when the set $\\{a_1,\\ldots,a_{m-1}\\}$ is $2$-distributable or $3$-distributable, $a_m=-1$, and $r=2$. 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