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QUESTION 4 - 1 POINT

Solve the inequality [tex]\frac{12n}{7}\ \textless \ 1[/tex], and write the solution in interval notation.

Provide your answer below:


Sagot :

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]