h) \( \frac{-7 x+4}{2}-\frac{x}{7}=x+\frac{5}{9} \)

To solve the equation \( \frac{-7x + 4}{2} - \frac{x}{7} = x + \frac{5}{9} \), first, we can eliminate the fractions by finding a common denominator. The least common multiple of 2, 7, and 9 is 126. Multiply each term of the equation by 126: \[ 126 \left( \frac{-7x + 4}{2} \right) - 126 \left( \frac{x}{7} \right) = 126 \left( x + \frac{5}{9} \right) \] This simplifies to: \[ 63(-7x + 4) - 18x = 126x + 70 \] Distributing and combining like terms gives: \[ -441x + 252 - 18x = 126x + 70 \] Combining the \(x\) terms on the left: \[ -459x + 252 = 126x + 70 \] Now, add \(459x\) to both sides: \[ 252 = 585x + 70 \] Subtract \(70\) from both sides: \[ 182 = 585x \] Now, dividing both sides by \(585\): \[ x = \frac{182}{585} \] This fraction can be simplified, but it means your solution is: \[ x \approx 0.3106 \; \text{(approximately)} \] And there you have your solution! Keep practicing similar problems to get even better at manipulating equations.