Question

Four more than the quotient of a number and three is at least nine

Answer 1

The question involves translating a verbal inequality into a mathematical one, resulting in the expression x/3 + 4 ≥ 9, which simplifies to x ≥ 15.

Step-by-step explanation:

The question 'Four more than the quotient of a number and three is at least nine' is a mathematical inequality problem. To translate this into an equation, we use the phrase 'the quotient of a number and three' to represent dividing a number by three. Adding 'four more' to this quotient implies an operation of addition after the division. 'At least nine' signifies that the result of this addition is nine or greater, which translates to an inequality. Therefore, the inequality statement in mathematical terms is x/3 + 4 ≥ 9.

To solve for x, we subtract 4 from both sides to get x/3 ≥ 5. Then, we multiply both sides by 3 to isolate x, which gives us x ≥ 15. This means that x must be 15 or a greater number to satisfy the inequality.

Answer 2

`(n)/(3) + 4 \geq 9 \\ (n)/(3) + (4-4) \geq (9-4) \\ (n)/(3) \geq 5 \\ (n)/(3)(3) \geq 5(3) \\ n \geq 15`