Final answer:
To solve the system of linear inequalities, solve each inequality separately and then find the intersection of their solution sets.
Step-by-step explanation:
To solve the system of linear inequalities {57x-7x > 3x-2; 22x-1 < 2x+47}, we will solve each inequality separately and then find the intersection of their solution sets.
Solving the first inequality: 57x - 7x > 3x - 2. Combined like terms, we get 50x > 3x - 2. Subtracting 3x from both sides, we have 47x > -2. Finally, dividing both sides by 47, we find that x > -2/47.
Solving the second inequality: 22x - 1 < 2x + 47. Again, combining like terms, we get 20x < 48. Dividing both sides by 20, we find that x < 48/20. Simplifying, x < 12/5.
Taking the intersection of the solution sets, we find that the solution to the system of inequalities is -2/47 < x < 12/5.