The sum of 4.6 and one-third a number is equal to at most 39.1. What are all the possible values of the number? Artem wrote the inequality 1/3n+4.6≤39.1

Question

, where n equals the number, to help solve this problem. Solve his inequality.(1 point)

Answer 1

To solve the inequality $\frac{1}{3}n+4.6\le 39.1$, we will first isolate $n$.

1. Subtract $4.6$ from both sides:

$$\frac{1}{3}n\le 39.1-4.6$$

2. Calculate $39.1-4.6$:

$$39.1-4.6=34.5$$

So, the inequality now is:

$$\frac{1}{3}n\le 34.5$$

3. Next, multiply both sides by $3$ to eliminate the fraction:

$$n\le 34.5\times 3$$

4. Calculate $34.5\times 3$:

$$34.5\times 3=103.5$$

Thus, the inequality simplifies to:

$$n\le 103.5$$

Therefore, all possible values of the number $n$ are:

$$n\in (-\mathrm{\infty },103.5]$$