(𝑥−4)(𝑥+3)≤0(x−4)(x+3)≤0

Sure, let's solve the inequality step by step:

1. First, set the inequality to zero: (x-4)(x+3) ≤ 0

2. Then, set each factor equal to zero and solve for x: x-4 = 0 and x+3 = 0. Solving these gives x = 4 and x = -3.

3. Now, we have three intervals to test on the number line: (-∞, -3), (-3, 4), and (4, ∞).

4. Choose a test point in each interval and substitute it into the inequality. If the inequality is true, the interval is part of the solution. If not, it is not part of the solution.

5. For (-∞, -3), choose x = -4. Substituting gives (-4-4)(-4+3) = 8 > 0, so this interval is not part of the solution.

6. For (-3, 4), choose x = 0. Substituting gives (0-4)(0+3) = -12 ≤ 0, so this interval is part of the solution.

7. For (4, ∞), choose x = 5. Substituting gives (5-4)(5+3) = 8 > 0, so this interval is not part of the solution.

8. Therefore, the solution to the inequality is -3 ≤ x ≤ 4.