13. The sum of six times a number and five is greater than the difference of three times a number and two. 14. The difference of twenty-seven and five times a number is less than or equal to four times a number.

13. Let's denote the unknown number as x. According to the given information, we can write the inequality as:<br /><br />6x + 5 > 3x - 2<br /><br />To solve this inequality, we need to isolate x. First, let's subtract 3x from both sides:<br /><br />6x - 3x + 5 > 3x - 3x - 2<br /><br />This simplifies to:<br /><br />3x + 5 > -2<br /><br />Next, let's subtract 5 from both sides:<br /><br />3x + 5 - 5 > -2 - 5<br /><br />This simplifies to:<br /><br />3x > -7<br /><br />Finally, let's divide both sides by 3:<br /><br />3x/3 > -7/3<br /><br />This simplifies to:<br /><br />x > -7/3<br /><br />So, the solution to the inequality is x > -7/3.<br /><br />14. Let's denote the unknown number as y. According to the given information, we can write the inequality as:<br /><br />27 - 5y ≤ 4y<br /><br />To solve this inequality, we need to isolate y. First, let's add 5y to both sides:<br /><br />27 - 5y + 5y ≤ 4y + 5y<br /><br />This simplifies to:<br /><br />27 ≤ 9y<br /><br />Next, let's divide both sides by 9:<br /><br />27/9 ≤ 9y/9<br /><br />This simplifies to:<br /><br />3 ≤ y<br /><br />So, the solution to the inequality is y ≥ 3.