Question

DAU 55 PUNCTE SI COROANA CLASA 6
.

.

.

.
.
$a) \: \: \frac{18}{8} = \frac{2x + 1}{x}$

$b) \: \: \frac{18}{12} = \frac{2x - 1}{x + 1}$

Answer 1

$a) \frac{18}{8} = \frac{2x + 1}{x}$

$\frac{9}{4} = \frac{2x + 1}{x}$

$9x = 4(2x + 1)$

$9x = 8x + 4$

$9x - 8x = 4$

$x = 4$

$b) \frac{18}{12} = \frac{2x - 1}{x + 1}$

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

$3(x + 1) = 2(2x - 1)$

$3x + 3 = 4x - 2$

$3x - 4x = - 2 - 3$

$- x = - 5 \: | \times ( - 1)$

$x = 5$

Answer 2

a) 18/8=(2x+1)/x    - aplicam proprietatea fundamentala a proportiilor
18x=8(2x+1)
18x=16x+8
18x - 16x=8
2x=8
x=8/2
x=4

b) 18/12=(2x-1)/(x+1)    - aplicam proprietatea fundamentala a proportiilor
12(2x-1)=18(x+1)
24x - 12=18x+18
24x - 18x=18+12
6x=30
x=30/6
x=5