Given that $$ n $$ is a whole number Such that $$ 12+7

Question

Given that $$ n $$ is a whole number Such that $$ 12+7<5 n+3 $$. List all the possible value of $$ n $$ if lt is less than 10 .

UpStudy AI · Accepted Answer

Sure, let's solve the inequality step by step and identify all possible whole number values of $$ n $$ that satisfy the conditions.

### Given:
1. $$ n $$ is a whole number.
2. $$ 12 + 7 < 5n + 3 $$
3. $$ n < 10 $$

### Step 1: Simplify the Inequality
Start by simplifying the inequality $$ 12 + 7 < 5n + 3 $$:

$$
19 < 5n + 3
$$

Subtract 3 from both sides to isolate the term with $$ n $$:

$$
19 - 3 < 5n
$$
$$
16 < 5n
$$

### Step 2: Solve for $$ n $$
Divide both sides of the inequality by 5:

$$
\frac{16}{5} < n
$$
$$
3.2 < n
$$

Since $$ n $$ is a whole number, the smallest integer greater than 3.2 is 4. Therefore:

$$
n \geq 4
$$

### Step 3: Apply the Upper Bound
We also have the condition that $$ n < 10 $$. Combining this with the lower bound:

$$
4 \leq n < 10
$$

### Step 4: List All Possible Whole Number Values of $$ n $$
The whole numbers that satisfy $$ 4 \leq n < 10 $$ are:

$$
n = 4, 5, 6, 7, 8, 9
$$

### Conclusion
All possible whole number values of $$ n $$ that satisfy the inequality $$ 12 + 7 < 5n + 3 $$ and are less than 10 are:

$$
\boxed{4,\ 5,\ 6,\ 7,\ 8,\ 9}
$$
The possible whole number values of $$ n $$ are 4, 5, 6, 7, 8, and 9.

Given that \( n \) is a whole number Such that \( 12+7<5 n+3 \). List all the possible value of \( n \) if lt is less than 10 .