Question

А) 3x-x²/2+2x²-x/6=x

Answer 1

Ответ:

x=23/9

Объяснение:

Answer 2

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

Step 1: Combine like terms on the left side of the equation: $3x - \frac{x^2}{2} + \frac{2x^2}{6} - \frac{x}{6} - x = 0$

Step 2: Find a common denominator for the fractions on the left side: $3x - \frac{3x^2}{6} + \frac{x^2}{6} - \frac{x}{6} - x = 0$

Step 3: Combine the fractions with a common denominator: $3x - \frac{3x^2 + x^2 - x}{6} - x = 0$

Step 4: Combine the numerators of the fractions: $3x - \frac{4x^2 - x}{6} - x = 0$

Step 5: Combine like terms in the numerator: $3x - \frac{4x^2 - x}{6} - x = 0$

Step 6: Multiply both sides of the equation by 6 to eliminate the fraction: $6(3x) - 6\left(\frac{4x^2 - x}{6}\right) - 6x = 0$

Step 7: Simplify: $18x - 4x^2 + x - 6x = 0$

Step 8: Combine like terms: $18x - 6x - 4x^2 + x = 0$

Step 9: Further simplify: $12x - 4x^2 = 0$

Step 10: Factor out a common factor of 4x: $4x(3 - x) = 0$

Now, set each factor equal to zero and solve for x:

1. $4x = 0$ Divide both sides by 4: $x = 0$

2. $3 - x = 0$ Add x to both sides: $3 = x$

So, the solutions to the equation are $x = 0$ and $x = 3$.