-(4x-7)%2F5x%2B9%3D2%2F3.jpeg "(3x+4)-(4x-7)/5x+9=2/3")
Solving the Equation (3x+4)-(4x-7)/5x+9=2/3
This article will guide you through the steps of solving the equation (3x+4)-(4x-7)/5x+9=2/3.
1. Simplifying the Equation
First, we need to simplify the equation by combining like terms and eliminating any parentheses:
- Distribute the negative sign: (3x+4) - (4x-7)/5x+9 = 2/3 becomes 3x + 4 - (4x/5x) + (7/5x) + 9 = 2/3
- Simplify the fractions: 3x + 4 - (4/5) + (7/5x) + 9 = 2/3
- Combine constant terms: 3x + 13 - (4/5) + (7/5x) = 2/3
2. Isolate the Variable
Now, our goal is to get all the terms with 'x' on one side of the equation and the constant terms on the other side:
- Subtract 13 from both sides: 3x - (4/5) + (7/5x) = -37/3
- Subtract (7/5x) from both sides: 3x - (4/5) = -37/3 - (7/5x)
3. Combine Like Terms
We need to combine the terms with 'x' on the right side of the equation:
- Find a common denominator for the right side: 3x - (4/5) = (-185 - 21x)/15
- Multiply both sides by 15: 45x - 12 = -185 - 21x
4. Solve for x
Now, we can solve for 'x':
- Add 21x to both sides: 66x - 12 = -185
- Add 12 to both sides: 66x = -173
- Divide both sides by 66: x = -173/66
Solution
Therefore, the solution to the equation (3x+4)-(4x-7)/5x+9=2/3 is x = -173/66.