Final answer:
To find the smallest integer value of x for the inequality -2x + 3 < -3, isolate x by subtracting 3 and dividing by -2, resulting in x > 3. The smallest integer value of x is therefore 4.
Step-by-step explanation:
To determine the smallest integer value of x in the solution of the inequality -2x + 3 < -3, we need to isolate x on one side of the inequality. Here are the steps to solve it:
- First, subtract 3 from both sides of the inequality: -2x + 3 - 3 < -3 - 3.
- This simplifies to: -2x < -6.
- Next, divide both sides by -2 to solve for x, and remember to reverse the inequality sign when dividing by a negative number: x > 3.
As we are looking for the smallest integer value of x, the answer would be 4 because x must be greater than 3.