Explicație pas cu pas:
a)
[tex] \frac{2x - 3}{4} - \frac{1 + x}{2} = 1.5 \\ \frac{2x - 3}{4} - \frac{2 \times (1 + x)}{2 \times 2} = \frac{6}{4} \\ 2x - 3 - 2(1 + x) = 6 \\ 2x - 3 - 2 - 2x = 6 \\ - 5 = 6 \\ nu \: exista \: solutii[/tex]
d)
[tex] \frac{x - 20}{5} = 1 - \frac{3x}{10} \\ \frac{2(x - 20)}{2 \times 5} = \frac{10}{10} - \frac{3x}{10} \\ 2x - 40 = 10 - 3x \\ 2x + 3x = 10 + 40 \\ 5x = 50 \\ x = 10[/tex]
e)
[tex](x - 2)(x + 2) = {(x - 2)}^{2} + 2(x - 4) \\ {x}^{2} - 4 = {x}^{2} - 4x + 4 + 2x - 8 \\ - 4 = - 2x - 4 \\ 2x = 0 \\ x = 0[/tex]
g)
[tex]2 \sqrt{3} (x - 2) - 2x( \sqrt{3} - 2) = x(4 - 2 \sqrt{3} ) \\ 2x \sqrt{3} - 4 \sqrt{3} - 2x \sqrt{3} + 4x = 4x - 2x \sqrt{3} \\ - 4 \sqrt{3} = - 2x \sqrt{3} \\ x = \frac{ - 4 \sqrt{3} }{ - 2 \sqrt{3} } \\ x = 2[/tex]
