To solve the inequality [tex]\( \frac{x}{4} > 12 \)[/tex], we need to isolate [tex]\( x \)[/tex] on one side of the inequality. Here is a step-by-step solution:
1. Start with the given inequality:
[tex]\[
\frac{x}{4} > 12
\][/tex]
2. Eliminate the fraction by multiplying both sides of the inequality by 4:
[tex]\[
\frac{x}{4} \times 4 > 12 \times 4
\][/tex]
3. Simplify both sides:
[tex]\[
x > 48
\][/tex]
Hence, the inequality [tex]\( \frac{x}{4} > 12 \)[/tex] has the same solution set as [tex]\( x > 48 \)[/tex]. This means any value of [tex]\( x \)[/tex] that is greater than 48 will satisfy the original inequality.
