Final answer:
To solve the compound inequality, subtract/add the necessary numbers and isolate the variable on one side of the inequality. Then, divide/multiply both sides, depending on the sign of the inequality.
Step-by-step explanation:
To solve the compound inequality 5x+11>=-9 and 10x-3<=27, we treat it as two separate inequalities and solve each one separately.
For 5x+11>=-9, we subtract 11 from both sides to isolate the x term: 5x > = -20. Then, we divide both sides by 5 to solve for x: x > = -4.
Next, for 10x-3<=27, we add 3 to both sides: 10x < = 30. Then, we divide both sides by 10 to solve for x: x < = 3.
Therefore, the solution to the compound inequality is -4 < = x < = 3.