Question

2x+(1/3x-1 1/9)*(-2 1/4)=-3/4

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To solve this equation, first distribute the terms on the left-hand side, and then simplify:

2x + (1/(3x - 1 1/9)) * (-2 1/4) = -3/4

Let's break it down step by step:

1. Calculate the value of (-2 1/4): -2 1/4 = -2 - 1/4 = -2 - 0.25 = -2.25

2. Rewrite the equation with the simplified value: 2x + (1/(3x - 1 1/9)) * (-2.25) = -3/4

3. Now, multiply both sides of the equation by (3x - 1 1/9) to eliminate the fraction in the denominator: (3x - 1 1/9) * (2x + (-2.25)) = -3/4 * (3x - 1 1/9)

4. Distribute on both sides of the equation: (3x - 1 1/9)(2x) + (3x - 1 1/9)(-2.25) = -3/4 * (3x - 1 1/9)

5. Now, multiply each term by its respective factor: (6x^2 - 2x) - (2.25(3x - 1 1/9)) = -3/4 * (3x - 1 1/9)

6. Distribute the -2.25 on the left side: 6x^2 - 2x - (2.25 * 3x) + 2.25 * (1 1/9) = -3/4 * (3x - 1 1/9)

7. Simplify the right side by multiplying -3/4 by each term: (6x^2 - 2x - 6.75x + 2.25(1 1/9)) = (-3/4 * 3x) + (-3/4 * (-1 1/9))

8. Further simplify the right side: (6x^2 - 2x - 6.75x + 2.25(10/9)) = (-9/4x) + (3/4 * (10/9))

9. Combine like terms on both sides: 6x^2 - 2x - 6.75x + 2.5 = (-9/4x) + (30/36)

10. Combine fractions on the right side: 6x^2 - 2x - 6.75x + 2.5 = (-9/4x) + (5/6)

11. To get rid of fractions, multiply both sides by 12 (the least common multiple of 4 and 6) to clear denominators: 12(6x^2 - 2x - 6.75x + 2.5) = 12((-9/4x) + (5/6))

12. Distribute 12 on both sides: 72x^2 - 24x - 81x + 30 = -27x + 20

13. Combine like terms on both sides: 72x^2 - 105x + 30 = -27x + 20

14. Move all terms to the left side to set the equation to zero: 72x^2 - 105x + 27x + 30 - 20 = 0

15. Combine like terms: 72x^2 - 78x + 10 = 0

Now you have a quadratic equation in standard form: 72x^2 - 78x + 10 = 0. To solve for x, you can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 72, b = -78, and c = 10. Plug these values into the formula and calculate the two possible solutions for x.