Using the given equation x/3 - 2/5 ÷ 3/4 - 2x = 16/15, we need to find the value of x.
- **Step 1: Simplify the equation**
- Convert the division to multiplication by taking the reciprocal of the fraction: x/3 - 2/5 * 4/3 - 2x = 16/15
- Simplify the fractions: x/3 - 8/15 - 2x = 16/15
- **Step 2: Get rid of the fractions**
- Multiply the entire equation by the least common denominator (LCD) of 15: 15(x/3) - 15(8/15) - 15(2x) = 15(16/15)
- This simplifies to: 5x - 8 - 30x = 16
- Combine like terms: -25x - 8 = 16
- **Step 3: Solve for x**
- Add 8 to both sides: -25x = 24
- Divide by -25: x = -24/25
- **Step 4: Verify the solution**
- Substitute the value of x back into the original equation:
- (-24/25)/3 - 2/5 ÷ 3/4 - 2(-24/25) = 16/15
- Simplify both sides and check if they are equal
Therefore, the solution to the equation x/3 - 2/5 ÷ 3/4 - 2x = 16/15 is x = -24/25.