Explicație pas cu pas:
1)
[tex]9x - 5(x + 4) = 7(x - 8) - 24 + x \\[/tex]
[tex]9x - 5x - 20 = 7x - 56 - 24 + x \\[/tex]
[tex]4x - 20 = 8x - 80 \\[/tex]
[tex]8x - 4x = 80 - 20 \\[/tex]
[tex]4x = 60 = > x = 15[/tex]
2)
[tex]\frac{3x + 1}{4} - \frac{7 - x}{2} - 2 = \frac{4x - 3}{3} - \frac{9 - 5x}{6} \\ [/tex]
[tex]3(3x + 1) - 6(7 - x) - 12 \times 2 = 4(4x - 3) - 2(9 - 5x) \\[/tex]
[tex]9x + 3 - 42 + 6x - 24 = 16x - 12 - 18 + 10x \\[/tex]
[tex]15x - 63 = 26x - 30 \\[/tex]
[tex]26x - 15x = 30 - 63 \\[/tex]
[tex]11x = - 33 = > x = - 3[/tex]
3)
[tex]0.5(2x + 7) - 0.3(3x - 8) = 0.9x - 0.2(3x - 5) + 1.3 \\ [/tex]
[tex]x + 3.5 - 0.9x + 2.4 = 0.9x - 0.6x + 1 + 1.3 \\ [/tex]
[tex]0.1x + 5.9 = 0.3x + 2.3 \\[/tex]
[tex]0.3x - 0.1x = 5.9 - 2.3 \\ [/tex]
[tex]0.2x = 3.6 = > x = 18[/tex]
4)
[tex]x\left( \frac{1}{1 \times 3} + \frac{1}{3 \times 5} + \frac{1}{5 \times 7} + ... + \frac{1}{61 \times 63} \right) = 2 - \frac{64}{63} \\ [/tex]
[tex] \frac{x}{2} \left( \frac{2}{1 \times 3} + \frac{2}{3 \times 5} + \frac{2}{5 \times 7} + ... + \frac{2}{61 \times 63} \right) = 2 - \frac{64}{63} \\ [/tex]
[tex]\frac{x}{2} \left( \frac{1}{1} - \frac{1}{3} + \frac{1}{3} - \frac{1}{5} + \frac{1}{5} - \frac{1}{7} + ... \frac{1}{61} - \frac{1}{63}\right) = \frac{2 \times 63 - 64}{63} \\ [/tex]
[tex]\frac{x}{2} \left( \frac{1}{1} - \frac{1}{63} \right) = \frac{62}{63} \\ [/tex]
[tex]\frac{x}{2} \times \frac{63 - 1}{63} = \frac{62}{63} \\[/tex]
[tex]\frac{x}{2} \times \frac{62}{63} = \frac{62}{63} \\[/tex]
[tex]\frac{x}{2} = 1 = > x = 1 \\ [/tex]
