$5\geq x\geq 10$ Please see image
Work Step by Step
$x+4\leq 9$ or $ x-3\geq 7\qquad$ ...solve each inequality separately. $ x+4\leq 9\qquad$ ...add $-4$ to each side of the inequality. $ x+4-4\leq 9-4\qquad$ ...simplify. $x\leq 5$ $ x-3\geq 7\qquad$ ...add $3$ to each side of the inequality. $ x-3+3\geq 7+3\qquad$ ...simplify. $x\geq 10$ The solutions are all real numbers that are less or equal to $5$ and greater or equal to $10$. Use solid dots on the number line to indicate $5$ and $10$ are solutions.