A.Divide both sides of the inequality by 6 to simplify: x/6 - 5/6
B.Divide both sides of the inequality by x to simplify: 1- 5/x <6
C.Multiply both sides of the inequality by x to simplify: x-5 < 6
D.Multiply both sides of the inequality by 6 to simplify: 6x-30 < x
A. To simplify the expression x/6 - 5/6, we can combine the fractions by finding a common denominator, which in this case is 6. The expression becomes (x - 5)/6.
B. To simplify the inequality 1 - 5/x < 6, we need to isolate x. We can do this by getting rid of the fraction on the left side. Multiply the entire inequality by x to get x - 5 < 6x. This is simplified by dividing both sides by 6: (x - 5)/6 < x.
C. To simplify the inequality x - 5 < 6, we can add 5 to both sides to isolate x: x - 5 + 5 < 6 + 5. This simplifies to x < 11.
D. To simplify the inequality 6x - 30 < x, we can start by subtracting x from both sides: 6x - x - 30 < 0. This further simplifies to 5x - 30 < 0. To isolate x, add 30 to both sides: 5x - 30 + 30 < 0 + 30. This simplifies to 5x < 30. Finally, divide both sides by 5 to solve for x: (5x)/5 < 30/5. This simplifies to x < 6.