Answer:
Explanation:
To solve the equation (5-2x)/3 + 1 - (3x-2)/5 = -x, we can follow these steps:
Step 1: Simplify the equation by getting rid of the fractions.
To eliminate the fractions, we can multiply each term by the least common multiple (LCM) of the denominators. In this case, the LCM of 3 and 5 is 15.
Multiply the first term (5-2x)/3 by 15/1:
(15/1) * (5-2x)/3 = (15/1) * (-x)
Simplify the multiplication on both sides:
5-2x = -15x
Multiply the second term 1 by 15/1:
(15/1) * 1 = (15/1) * (-x)
Simplify the multiplication on both sides:
15 = -15x
Multiply the third term (3x-2)/5 by 15/1:
(15/1) * (3x-2)/5 = (15/1) * (-x)
Simplify the multiplication on both sides:
3x-2 = -15x
Step 2: Combine like terms and isolate the variable.
Rearrange the equation by moving all the terms with x to one side and the constant terms to the other side.
Start by adding 15x to both sides of the equation:
5-2x + 15x = -15x + 15x
Simplify:
5 + 13x = 0
Next, move the constant term 5 to the other side by subtracting 5 from both sides:
5 + 13x - 5 = 0 - 5
Simplify:
13x = -5
Finally, divide both sides of the equation by 13 to solve for x:
(13x)/13 = (-5)/13
Simplify:
x = -5/13
So, the solution to the equation (5-2x)/3 + 1 - (3x-2)/5 = -x is x = -5/13.