Question

3x-(2x+3)/2 = (x+6)/3

Answer 1

Ответ:

$x = 0,3.$

Пошаговое объяснение:

$3x-\frac{2x+3}{2} = \frac{x+6}{3}$

$\frac{3x*6}{1*6} -\frac{3(2x+3)}{2*3} = \frac{2(x+6)}{3*2}$

$\frac{18x}{6} - \frac{6x+9}{6} = \frac{2x+12}{6}$

$\frac{18x*6}{6} - \frac{6(6x+9)}{6} = \frac{6(2x+12)}{6}$

(знаменатели сокращаются)

$18x-6x+9=2x+12$

$18x -6x-2x=12-9$

$10x=3$

$x = 3:10$

$x = 0,3.$

$:)$

Answer 2

To solve the equation $3x - \frac{{2x + 3}}{2} = \frac{{x + 6}}{3}$, follow these steps:

Step 1: Distribute the denominator on the left side:

$3x - \frac{{x + 3}}{1} = \frac{{x + 6}}{3}$

Step 2: Eliminate the fractions by multiplying through by the least common denominator, which is 6:

$6 \cdot 3x - 6 \cdot \frac{{x + 3}}{1} = 6 \cdot \frac{{x + 6}}{3}$

This simplifies to:

$18x - 6(x + 3) = 2(x + 6)$

Step 3: Distribute on both sides:

$18x - 6x - 18 = 2x + 12$

Step 4: Combine like terms:

$12x - 18 = 2x + 12$

Step 5: Move all terms involving $x$ to one side and constants to the other side:

$12x - 2x = 12 + 18$

This simplifies to:

$10x = 30$

Step 6: Divide both sides by 10:

$x = 3$

So, the solution to the equation is $x = 3$.