Which of the following equations has the correct solution? x-7=8;x=1 (x)/(5)=15;x=3 C 3(x-1)=6;x=3 (1)/(2)x+5=9;x=2

Let's solve each equation step by step to determine which one has the correct solution:<br /><br />A) $x - 7 = 8$<br />To solve for $x$, we need to isolate it on one side of the equation. We can do this by adding 7 to both sides of the equation:<br />$x - 7 + 7 = 8 + 7$<br />Simplifying, we get:<br />$x = 15$<br /><br />B) $\frac{x}{5} = 15$<br />To solve for $x$, we need to isolate it on one side of the equation. We can do this by multiplying both sides of the equation by 5:<br />$\frac{x}{5} \times 5 = 15 \times 5$<br />Simplifying, we get:<br />$x = 75$<br /><br />C) $3(x - 1) = 6$<br />To solve for $x$, we need to distribute the 3 to the terms inside the parentheses:<br />$3x - 3 = 6$<br />Next, we add 3 to both sides of the equation:<br />$3x - 3 + 3 = 6 + 3$<br />Simplifying, we get:<br />$3x = Finally, we divide both sides of the equation by 3:<br />$\frac{3x}{3} = \frac{9}{3}$<br />Simplifying, we get:<br />$x = 3$<br /><br />D) $\frac{1}{2}x + 5 = 9$<br />To solve for $x$, we need to isolate it on one side of the equation. We can do this by subtracting 5 from both sides of the equation:<br />$\frac{1}{2}x + 5 - 5 = 9 - 5$<br />Simplifying, we get:<br />$\frac{1}{2}x = 4$<br />Finally, we multiply both sides of the equation by 2 to solve for $x$:<br />$\frac{1}{2}x \times 2 = 4 \times 2$<br />Simplifying, we get:<br />$x = 8$<br /><br />Comparing the solutions for each equation, we can see that the correct solution is option C: $3(x - 1) = 6; x = 3$.