Equation solve help?

[Guest]

Hi
Could someone please help explain how to solve x in this equation, where all c1 to c3 are constants?

c1 = x•c2 + (1-x)•c3

[ammornil]

Hi
Could someone please help explain how to solve x in this equation, where all c1 to c3 are constants?

c1 = x•c2 + (1-x)•c3

[tex]c_{1} = c_{2}.x+c_{3}.(1-x) \Leftrightarrow c_{2}.x+c_{3}.1-c_{3}.x = c_{1} \Leftrightarrow (c_{2}-c_{3}).x=c_{1} -c_{3} \Rightarrow x=\frac{c_{1} -c_{3}}{c_{2}-c_{3}}[/tex]

[Guest]

Same thing, written "prettier":

[tex]c_2x+ c_3(1- x)= c_1[/tex]
Expand the parentheses:
[tex]c_2x+ c_3- c_3x= c_1[/tex]
Subtract [tex]c_3[/tex] from both sides:
[tex]c_2x- c_3x= c_1- c_3[/tex]
Factor out "x" on the left:
[tex](c_2- c_3)x= c_1- c_3[/tex]
Divide both sides by [tex]c_2- c_3[/tex]:

[tex]x=\frac{c_1- c_3}{c_2- c_3}[/tex]