Question

3x+2/6+3x-2/4=2x-1/3-5/2

Answer 1

6x-2x=-1/3-5/2+2/4-2/6
4x=-4/12-30/12+6/12-4/12
4x=-32
x=-8

Answer 2

To solve the equation, we need to combine like terms and then isolate the variable (x). Let's go step by step:

1. Combine the like terms on both sides of the equation: The left side has two fractions that need to be simplified: (3x + 2)/6 + (3x - 2)/4 = (2x - 1)/3 - 5/2

   To add fractions with different denominators, we need to find a common denominator. The common denominator for 6 and 4 is 12. So, we'll rewrite the fractions with the common denominator:

   ((3x + 2) * 2)/12 + ((3x - 2) * 3)/12 = ((2x - 1) * 4)/12 - (5 * 6)/12

   Simplify the fractions:

   (6x + 4)/12 + (9x - 6)/12 = (8x - 4)/12 - 30/12

2. Now, combine the numerators on both sides: (6x + 4 + 9x - 6)/12 = (8x - 4 - 30)/12

3. Combine like terms again: (15x - 2)/12 = (8x - 34)/12

4. Now, we'll eliminate the denominators by multiplying both sides by 12: 12 * (15x - 2)/12 = 12 * (8x - 34)/12

   This results in:

   15x - 2 = 8x - 34

5. Let's isolate the variable (x) on one side of the equation. To do that, we'll move the 8x term to the left side by subtracting 8x from both sides, and move the constant terms to the right side by adding 34 to both sides:

   15x - 8x - 2 = 8x - 8x - 34

   Simplify:

   7x - 2 = -34

6. Now, isolate the x term by moving the constant term to the right side. Add 2 to both sides:

   7x = -34 + 2

   7x = -32

7. Finally, divide both sides by 7 to solve for x:

   x = -32 / 7

So, the solution to the equation is:

x = -32 / 7