the question says solve for x


x+3/5+4x/15=x-7/3

x+4x/15-x=-7/3-3/5 (bringing like terms together)

4x/15=-7/3-3/5 (Make the denominator common by multipying 3 with 5 and 5 by 3)(Also multiply the numerator by the same numbers)
4x/15=-35-9/15(15 cancels out on both sides)
4x=-44 (divide 44 by 4)
x=-11

I don't like fractions and if I can avoid them , I will

multiply each term by the LCD, in this case 15
15x + 9 + 4x = 15x - 35
4x = -44
x = -11

I have a strange feeling that you meant:

(x+3)/5 + 4x/15 = (x-7)/3
again, times 15
3(x+3) + 4x = 5(x-7)
3x + 9 + 4x = 5x - 35
2x = -44
x = -22

See what difference brackets make and how critical it is to have them?

To solve for x in the equation x + 3/5 + 4x/15 = x - 7/3, we can follow these steps:

Step 1: Clear the denominators.
In order to work with fractions more easily, we need to eliminate the denominators. We can do this by multiplying every term in the equation by the least common multiple (LCM) of the denominators. In this case, the LCM of 5, 15, and 3 is 15.

Multiply each term by 15:
15(x) + 15(3/5) + 15(4x/15) = 15(x) + 15(-7/3)

Simplifying, we get:
15x + 9 + 4x = 15x - 35/3

Step 2: Combine like terms.
Combine the x-terms on both sides of the equation and combine the constant terms on both sides.

15x + 4x = 15x (on the left side)
9 = - 35/3

Step 3: Isolate the variable.
We want to isolate the variable on one side of the equation. Since we have x terms on both sides, we can subtract 15x from both sides to eliminate it.

15x - 15x + 4x = 15x - 15x (on the left side)
9 - 15x = - 35/3 - 15x

Simplifying, we get:
4x = 0 - 35/3

Step 4: Combine and simplify the constant terms.

4x = - 35/3 (on the left side)

Step 5: Solve for x.
Finally, we can solve for x by dividing both sides of the equation by 4:

(4x)/4 = (-35/3)/4 (divide both sides by 4)

Simplifying, we get:
x = -35/12

Therefore, the solution to the equation x + 3/5 + 4x/15 = x - 7/3 is x = -35/12.