Solve $3 x-7 \leq 5 x+13$

Step 1 ：Given the inequality \(3x - 7 \leq 5x + 13\)

Step 2 ：Subtract 3x from both sides to get \(-2x - 7 \leq 13\)

Step 3 ：Add 7 to both sides to get \(-2x \leq 20\)

Step 4 ：Divide both sides by -2 to get \(x \geq -10\)

Step 5 ：Check the solution in the original inequality \(3x - 7 \leq 5x + 13\)

Step 6 ：Substitute x = -10 into the inequality to get \(3(-10) - 7 \leq 5(-10) + 13\)

Step 7 ：Simplify to get \(-30 - 7 \leq -50 + 13\)

Step 8 ：Simplify further to get \(-37 \leq -37\)

Step 9 ：Since the inequality holds true, the solution is valid

Step 10 ：\(\boxed{x \geq -10}\) is the solution to the inequality \(3x - 7 \leq 5x + 13\)