Final answer:
To solve the inequality 3x-1 ≤ 35+9x, isolate the variable x on one side of the inequality by performing operations on both sides. The greatest integer solution is -6, confirming Albert's claim.
Step-by-step explanation:
To solve the inequality 3x-1 ≤ 35+9x, we need to isolate the variable x on one side of the inequality.
Starting with the given inequality: 3x-1 ≤ 35+9x
First, we can subtract 3x from both sides to eliminate the 3x term from the left side: -1 ≤ 35+6x
Next, we can subtract 35 from both sides to isolate the variable term: -1-35 ≤ 6x
Combining like terms: -36 ≤ 6x
Finally, we can divide both sides by 6 to solve for x: -6 ≤ x
Therefore, Albert is correct in claiming that -6 is the greatest integer solution of the inequality.