If three times a number added to 4 is divided by the number plus 6, the result is five halves Find the number. The number is square

Let's denote the unknown number as \( x \).<br /><br />According to the problem, three times the number added to 4 is divided by the number plus 6, and the result is five halves. We can write this relationship as an equation:<br /><br />\[<br />\frac{3x + 4}{x + 6} = \frac{5}{2}<br />\]<br /><br />To solve for \( x \), we will cross-multiply to eliminate the fraction:<br /><br />\[<br />2(3x + 4) = 5(x + 6)<br />\]<br /><br />Expanding both sides of the equation gives:<br /><br />\[<br />6x + 8 = 5x + 30<br />\]<br /><br />Next, we'll isolate \( x \) by subtracting \( 5x \) from both sides:<br /><br />\[<br />6x - 5x + 8 = 30<br />\]<br /><br />Simplifying, we have:<br /><br />\[<br />x + 8 = 30<br />\]<br /><br />Subtract 8 from both sides to solve for \( x \):<br /><br />\[<br />x = 22<br />\]<br /><br />Thus, the number is \( \boxed{22} \).