Final answer:
The smallest integer value for x that satisfies the inequality 4x + 3 ≤ -11 is -4.
Step-by-step explanation:
To find the smallest integer value of x where 4x + 3 ≤ -11, you first need to solve the inequality. Subtract 3 from both sides to get 4x ≤ -14. Then, divide both sides by 4 to get x ≤ -3.5. Since we are looking for the smallest integer value of x that satisfies the inequality, and integers are whole numbers, the smallest integer less than or equal to -3.5 is -4.
Thus, the smallest integer value for x that makes the expression 4x + 3 ≤ -11 true is -4.