To solve the inequality [tex]\(\frac{12n}{7} < 1\)[/tex], let's go through the steps in a detailed manner.
### Step 1: Isolate [tex]\(n\)[/tex]
We start with the inequality:
[tex]\[
\frac{12n}{7} < 1
\][/tex]
### Step 2: Eliminate the fraction
To eliminate the fraction, we can multiply both sides of the inequality by 7, which is the denominator:
[tex]\[
7 \cdot \frac{12n}{7} < 7 \cdot 1
\][/tex]
This simplifies to:
[tex]\[
12n < 7
\][/tex]
### Step 3: Solve for [tex]\(n\)[/tex]
Next, solve for [tex]\(n\)[/tex] by dividing both sides of the inequality by 12:
[tex]\[
n < \frac{7}{12}
\][/tex]
### Step 4: Write the solution in interval notation
The solution to the inequality [tex]\(n < \frac{7}{12}\)[/tex] is the set of all real numbers [tex]\(n\)[/tex] that are less than [tex]\(\frac{7}{12}\)[/tex].
In interval notation, this is written as:
[tex]\[
(-\infty, \frac{7}{12})
\][/tex]
So, the solution to the inequality [tex]\(\frac{12n}{7} < 1\)[/tex] is:
[tex]\[
(-\infty, \frac{7}{12})
\][/tex]
