Question

2/3x-1/18x+1/2=2 2/9​

Answer 1

Ответ:

$\\ \\ \frac{2}{3x} - \frac{1}{18x} + \frac{1}{2} = 2 \frac{2}{9} →odz \: x≠0 \: \\ \\ \frac{2}{3x} - \frac{1}{18x} + \frac{1}{2} = \frac{20}{9} \\ \\ \frac{2}{3x} - \frac{1}{18x} = \frac{20}{9} - \frac{1}{2} \\ \\ \frac{6 \times 2}{6 \times 3x} - \frac{1}{18x} = \frac{20}{9} - \frac{1}{2} \\ \\ \frac{12}{18x} - \frac{1}{18x} = \frac{20}{9} - \frac{1}{2} \\ \\ \frac{11}{18x} = \frac{20}{9} - \frac{1}{2} \\ \\ \frac{11}{18x} = \frac{40}{18} - \frac{9}{18} \\ \\ \frac{11}{18x} = \frac{31}{18} \\ \\ 11 \times 18 = 31 \times 18x \\ \\ 198 = 558x \\ \\ 558x = 119 \\ \\ x = \frac{119}{558} \\ \\ x = \frac{11}{31} .odz \: x≠o$

Ответ: x=11/31 ,значение не было задано в ОДЗ

Answer 2

To solve the equation (2/3)x - (1/18)x + 1/2 = (2/9), we can start by simplifying the left side of the equation:

(2/3)x - (1/18)x + 1/2 = 2/9

To add or subtract fractions, we need a common denominator. The least common multiple (LCM) of 3, 18, and 2 is 18. Therefore, we can rewrite the fractions with the denominator of 18:

(12/18)x - (1/18)x + 9/18 = 2/9

Now, let's combine the x terms on the left side:

(12/18 - 1/18)x + 9/18 = 2/9

Simplifying the coefficients:

(11/18)x + 9/18 = 2/9

Next, we can simplify the right side of the equation:

9/18 is equivalent to 1/2, and 2/9 is already in its simplest form. So we have:

(11/18)x + 1/2 = 2/9

To eliminate the fraction on the left side, we can multiply the entire equation by the common denominator of 18:

18 * [(11/18)x + 1/2] = 18 * (2/9)

This yields:

11x + 9 = 4

Next, we isolate the x term by subtracting 9 from both sides of the equation:

11x = 4 - 9 11x = -5

Finally, we solve for x by dividing both sides of the equation by 11:

x = -5/11

Therefore, the solution to the equation (2/3)x - (1/18)x + 1/2 = (2/9) is x = -5/11.