Question

Se considera ecuatia

$\frac{x + 2}{3} - \frac{x - a}{4} = 1$
a apartinand numerelor reale.

a)Rezolvati ecuatia pentru a=1
b)Determinati valoarea lui a astfel incat numarul 2 sa fie solutie a ecuatiei​

Answer 1

a)

$\frac{x + 2}{3} - \frac{x - 1}{4} = 1$

$\frac{4 \times (x + 2)}{12} - \frac{3 \times (x - 1)}{12} = \frac{12}{12}$

$4x + 8 - (3x - 3) = 12$

$4x + 8 - 3x + 3 = 12$

$x = 12 - 11 = 1$

b)

$\frac{2+ 2}{3} - \frac{2- a}{4} = 1$

$\frac{4 \times 4}{12} - \frac{3 \times (2- a)}{12} = \frac{12}{12}$

$16 - (6 - 3a) = 12$

$16 - 6 + 3a = 12$

$3a = 12 - 10 = 2$

$a = \frac{2}{3}$