Question

Solve the equation: 2 - 8/3 = (x - 2)/15.

Answer 1

`To solve the equation \(2 - (8)/(3) = (x - 2)/(15)\), follow these steps:1. Start by simplifying both sides of the equation: \(2 - (8)/(3) = (x - 2)/(15)\) To subtract \((8)/(3)\) from 2, you'll need a common denominator, which is 3. So, rewrite 2 as \((6)/(3)\): \((6)/(3) - (8)/(3) = (x - 2)/(15)\)2. Combine the fractions on the left side: \((6 - 8)/(3) = (x - 2)/(15)\) \((-2)/(3) = (x - 2)/(15)\)`

`3. Cross-multiply to isolate the \(x - 2\) term: \(-2 \cdot 15 = 3 \cdot (x - 2)\) \(-30 = 3x - 6\)4. Add 6 to both sides to isolate the \(3x\) term: \(-30 + 6 = 3x\) \(-24 = 3x\)5. Finally, divide both sides by 3 to solve for \(x\): \((-24)/(3) = x\) \(-8 = x\)So, the solution to the equation is \(x = -8\).`