Final answer:
To solve the given inequality, set up the inequality 7x - 2 ≤ 3x - 6. Simplify the inequality by subtracting 3x and adding 2 to both sides. Divide both sides by 4 to solve for x and find that the solution set is x ≤ -1.
Step-by-step explanation:
To translate the given statement into an inequality, we can set up the inequality: 7x - 2 ≤ 3x - 6. This inequality states that the product of a number (represented by x) and 7, decreased by 2, is at most 6 less than three times the number.
To solve the inequality, we can start by subtracting 3x from both sides: 7x - 3x - 2 ≤ 3x - 3x - 6. This simplifies to 4x - 2 ≤ -6.
Next, we can add 2 to both sides: 4x - 2 + 2 ≤ -6 + 2. This gives us 4x ≤ -4.
Finally, we can divide both sides by 4 to solve for x: (4x)/4 ≤ -4/4. This simplifies to x ≤ -1. Therefore, the solution set for the inequality is x ≤ -1.