Final answer:
The statement "twelve times a number minus thirty is less than or equal to eighteen" can be expressed as the inequality '12x - 30 ≤ 18'. By adding 30 to both sides and then dividing by 12, we get the solution 'x ≤ 4'.
Step-by-step explanation:
To express the statement "twelve times a number minus thirty is less than or equal to eighteen" as an equation, we will first introduce a variable to represent the unknown number.
Let's use 'x' for this purpose. So, the phrase "twelve times a number" can be translated to '12x'. Now, we include "minus thirty," which gives us '12x - 30'. The phrase "is less than or equal to eighteen" tells us to use the less than or equal sign (≤) followed by 18. Thus, the final inequality is '12x - 30 ≤ 18'.
To solve this inequality, we'll perform operations that maintain the equality, according to LibreTexts. We need to isolate 'x', so we add thirty to both sides of the inequality which gives us '12x ≤ 48'. Then we divide both sides by twelve.
Remember, dividing by a positive number does not change the direction of the inequality. So we get 'x ≤ 4' as the final answer.