Final answer:
The mathematical inequality for the statement 'twice the difference of a number and 4 is at least 29' is '2(x - 4) ≥ 29.' To solve for the number, distribute 2 across the parentheses, add 8 to both sides, and then divide by 2, resulting in the solution x ≥ 18.5.
Step-by-step explanation:
The phrase 'twice the difference of a number and 4 is at least 29' can be translated into a mathematical inequality. To model this, let 'x' represent the unknown number. The 'difference of a number and 4' is written as 'x - 4.' Twice this difference is '2(x - 4)'. That this amount is 'at least 29' tells us the inequality is '2(x - 4) ≥ 29.' To solve for 'x', we follow these steps:
- Distribute the 2 across the parentheses: 2x - 8 ≥ 29.
- Add 8 to both sides to isolate the term with the variable: 2x ≥ 29 + 8, which simplifies to 2x ≥ 37.
- Divide both sides by 2 to solve for x: x ≥ 18.5.
This inequality tells us that the number must be 18.5 or greater to satisfy the condition that 'twice the difference of a number and 4 is at least 29.'