Question

2x+7/3 - x-3/2 = 4x​

Answer 1

Ответ:

$x = 1$

Пошаговое объяснение:

$\frac{2x + 7}{3} - \frac{x - 3}{2} = 4x \\ 2(2x + 7) - 3(x - 3) = 24x \\ 4x + 14 - 3x + 9 = 24x \\ x + 23 = 24x \\ x - 24x = - 23 \\ - 23x = - 23 \\x = \frac{ - 23}{ - 23} \\ x = 1$

Answer 2

To solve the equation, we need to simplify and isolate the variable "x" on one side of the equation. Let's start step-by-step:

1. Combine like terms on both sides of the equation: (2x + 7)/3 - (x - 3)/2 = 4x

To do this, we need to find a common denominator for the fractions, which is 6.

2. Convert (2x + 7)/3 to a fraction with a denominator of 6: [(2x + 7)/3] * [2/2] = (2(2x + 7))/6 = (4x + 14)/6

3. Convert (x - 3)/2 to a fraction with a denominator of 6: [(x - 3)/2] * [3/3] = (3(x - 3))/6 = (3x - 9)/6

Now, the equation becomes: (4x + 14)/6 - (3x - 9)/6 = 4x

4. Combine the fractions on the left side: (4x + 14 - (3x - 9))/6 = 4x

5. Distribute the negative sign on the right side: (4x + 14 - 3x + 9)/6 = 4x

6. Combine like terms again: (x + 23)/6 = 4x

7. Now, to isolate "x," we'll get rid of the fraction. Multiply both sides of the equation by 6 to eliminate the denominator: 6 * (x + 23)/6 = 6 * 4x

The 6 on the left side cancels out with the denominator: x + 23 = 24x

8. Move all terms containing "x" to one side of the equation and constant terms to the other side. Let's move "x" terms to the left side and constants to the right side: x - 24x = -23

9. Combine like terms: -23x = -23

10. Finally, solve for "x" by dividing both sides by -23: x = -23 / -23

x = 1

Thus, the solution to the equation is x = 1.