[tex]a) \frac{4y-5}{28}= \frac{3y+15}{36} [/tex]
utilizam proprietatea proportiilor: produsul mezilor=produsul extremelor
[tex]36(4y-5)=28(3y+15) \\ \\ 144y-36\cdot5=84y+15\cdot28 \\ \\ 144y-84y=420-180 \\ \\ 60y=240 \\ \\ y=240:60 \\ \\ y=4[/tex]
[tex]b) \frac{3y-7}{15}= \frac{2y-6}{9} [/tex]
utilizam proprietatea proportiilor: produsul mezilor=produsul extremelor
[tex]9(3y-7)=15(2y-6) \\ \\27y-9\cdot7=30y-15\cdot6 \\ \\ -63+90=30y-27y \\ \\ 27=3y \\ \\ y=9[/tex]
[tex]c) \frac{4y-5}{3y+8}= \frac{3}{14} [/tex]
utilizam proprietatea proportiilor: produsul mezilor=produsul extremelor
[tex]14(4y-5)=3(3y+8) \\ \\ 56y-70=9y+24 \\ \\ 56y-9y=24+70 \\ \\ 47y=94 \\ \\ y=2[/tex]
[tex]d) \frac{4y+11}{5y-9}= \frac{3}{2} [/tex]
utilizam proprietatea proportiilor: produsul mezilor=produsul extremelor
[tex]2(4y+11)=3(5y-9) \\ \\8y+22=15y-27 \\ \\ 22+27=15y-8y \\ \\49=7y \\ \\ y=49:7=7[/tex]
[tex]e)\frac{6y+11}{5y+8}= 1,2(7) \\ \\ 1,2(7)= \frac{127-12}{90}= \frac{115}{90} \\ \\ \frac{6y+11}{5y+8}= \frac{115}{90} \\ \\ 90(6y+11)=115(5y+8) \\ \\ 540y+990=575y+920 \\ \\ 575y-540y=990-920 \\ \\ 35y=70 \\ \\ y=2[/tex]
