Final answer:
The mathematical expression for the statement 'eleven is at least three times the difference of double a number x and four' is written as the inequality 11 >= 3(2x - 4). After simplifying, we find that x <= 23/6 or approximately 3.8333.
Step-by-step explanation:
The question asks to express a mathematical statement: What is eleven is at least three times the difference of double a number x and four?
This can be translated into an inequality.
The phrase 'at least' suggests that we are dealing with a minimum value, so we use the ≥ symbol for 'greater than or equal to'.
'Three times the difference of double a number x and four' means 3 multiplied by the difference between 2 times a number (which we will call x) and 4.
Therefore, the complete inequality is 11 ≥ 3(2x - 4).
Next, let's simplify and solve for x:
- Multiply the difference by 3: 11 ≥ 6x - 12.
- Add 12 to both sides of the inequality: 11 + 12 ≥ 6x, which simplifies to 23 ≥ 6x.
- Finally, divide both sides by 6 to solve for x: x ≤ 23/6 or approximately 3.8333.