Răspuns:
[tex]\boldsymbol{ \red{S = \bigg\{\dfrac{61}{5} \bigg\} }}[/tex]
Explicație pas cu pas:
[tex]\dfrac{5x}{12} - \dfrac{3x + 1}{8} = \dfrac{4x - 3}{9} - \dfrac{2x + 3}{6} - \dfrac{5}{36}\\[/tex]
Aducem la același numitor
12=2²·3, 8=2³, 9=3², 6=2·3, 36=2²·3²
Numitorul comun este 2³·3²=8·9=72
[tex]\dfrac{^{6)} 5x}{12} - \dfrac{^{9)} 3x + 1}{8} = \dfrac{^{8)} 4x - 3}{9} - \dfrac{^{12)} 2x + 3}{6} - \dfrac{^{2)} 5}{36}\\[/tex]
[tex]6 \cdot 5x - 9(3x+1) = 8(4x-3)-12(2x+3)-2\cdot5\\[/tex]
[tex]30x - 27x - 9 = 32x - 24 - 24x - 36 - 10\\[/tex]
[tex]3x - 9 = 8x - 70 \implies 70 - 9 = 8x - 3x\\[/tex]
[tex]5x = 61 \implies \bf x = \dfrac{61}{5}[/tex]
