Respuesta :
The inequality to represent “7 less than the product of a number, n, and 1/6 is at most 45” is:
[tex]\frac{n}{6} - 7 \leq 45[/tex]
Solution:
Let the number be "n"
From given,
7 less than product of a number n and 1/6 is at most 45
At most means "less than or equal to"
Therefore, inequality is framed as:
[tex](n \times \frac{1}{6}) - 7 \leq 45[/tex]
Thus, inequality is:
[tex]\frac{n}{6} - 7 \leq 45[/tex]
Solve the inequality
[tex]\mathrm{Add\:}7\mathrm{\:to\:both\:sides}\\\\\frac{n}{6}-7+7\le \:45+7\\\\simplify\\\\\frac{n}{6}\le \:52\\\\\mathrm{Multiply\:both\:sides\:by\:}6\\\\\frac{6n}{6}\le \:52\cdot \:6\\\\simplify\\\\n \le \:312[/tex]
Thus the inequality is solved
