%2F5%2B8%2F5%3D3(x-1).jpeg "(-2x-4)/5+8/5=3(x-1)")
Solving the Equation: (-2x-4)/5+8/5=3(x-1)
This article will guide you through the steps of solving the equation (-2x-4)/5+8/5=3(x-1). We will break down each step to ensure a clear understanding of the solution process.
1. Simplifying the Equation
- Combine like terms: On the left side of the equation, notice that both fractions have a common denominator of 5. Combine the numerators: (-2x - 4 + 8)/5 = 3(x-1) This simplifies to: (-2x + 4)/5 = 3(x-1)
- Distribute on the right side: Expand the right side of the equation by multiplying 3 with each term inside the parenthesis: (-2x + 4)/5 = 3x - 3
2. Eliminating Fractions
- Multiply both sides by the denominator: To eliminate the fraction on the left side, multiply both sides of the equation by 5: 5 * [(-2x + 4)/5] = 5 * (3x - 3) This simplifies to: -2x + 4 = 15x - 15
3. Isolating the Variable
- Combine x terms: Add 2x to both sides of the equation to move all x terms to the right side: 4 = 17x - 15
- Combine constant terms: Add 15 to both sides of the equation to isolate the x term: 19 = 17x
4. Solving for x
- Divide both sides by the coefficient of x: Divide both sides of the equation by 17 to solve for x: 19/17 = x
Therefore, the solution to the equation (-2x-4)/5+8/5=3(x-1) is x = 19/17.