Question

ma puteti ajuta va rog?
1. x+3/2 +x-2/4=5/6
2. 2x-3/8-3x-2/4=x+1/2
3. 5x+1/3-2x-1/6+3x/2=1
4. x+2/5-x-2/10+2x-3/2=x

Answer 1

1.

$\frac{x + 3}{2} + \frac{x - 2}{4} = \frac{5}{6} \\ inmultim \: ambele \: parti \: ale \\ ecuatiei \: cu \: 12 \\ 6(x + 3) + 3(x - 2) = 10 \\ 6x + 18 + 3x - 6 = 10 \\ 9x + 12 = 10 \\ 9x = 10 - 12 \\ 9x = - 2 \\ x = - \frac{2}{9}$

2.

$\frac{2x - 3}{8} - \frac{3x - 2}{4} = \frac{x + 1}{2} \\ inmultim \: ambele \: parti \: ale \: \\ ecuatiei \: cu \: 8 \\ 2x - 3 - 2(3x - 2) = 4(x + 1) \\ 2x - 3 - 6x + 4 = 4x + 4 \\ 2x - 3 - 6x = 4x \\ - 4x - 4x = 3 \\ - 8x = 3 \\ x = - \frac{3}{8}$

3.

$\frac{5x + 1}{3} - \frac{2x - 1}{6} + \frac{3x}{2} = 1 \\ inmulteste \: ambele \: parti \: ale \\ ecuatiei \: cu \: 6 \\ 2(5x + 1) - (2x - 1) + 9x = 6 \\ 10x + 2 - 2x + 1 + 9x = 6 \\ 17x + 3 = 6 \\ 17x = 3 \\ x = \frac{3}{17}$

4.

$\frac{x + 2}{5} - \frac{x - 2}{10} + \frac{2x - 3}{2} = x \\ inmultim \: ambele \: parti \: ale \: \\ ecuatiei \:cu \: 10 \\ 2(x + 2) - (x - 2) + 5(2x - 3) = 10x \\ 2x + 4 - (x - 2) + 10x - 15 = 10x \\ 2x + 4 - (x - 2) - 15 = 0 \\ 2x + 4 - x + 2 - 15 = 0 \\ x - 9 = 0 \\ x = 9$