Final answer:
The integral values of x which satisfy the inequality x² - x ≤ 12, after solving the quadratic inequality, are -3, -2, -1, 0, 1, 2, 3, and 4. These values are found by factoring the quadratic equation and including all integers within the boundary points -3 and 4.
Step-by-step explanation:
To find the integral values of x which satisfy the inequality x² - x ≤ 12, we first rearrange it to x² - x - 12 ≤ 0. This is a quadratic inequality, and we can solve it by factoring the quadratic equation or using the quadratic formula if factoring is not possible.
The factored form of the quadratic equation is (x - 4)(x + 3) ≤ 0.
We then set each factor to zero to find the boundary points of the inequality, which are x = 4 and x = -3.
The solution to the inequality will be the set of x values between these boundary points, including the points themselves, since the inequality symbol is '≤'.
A number line or sign analysis can help determine which regions satisfy the inequality. The integral values that satisfy the inequality are: -3, -2, -1, 0, 1, 2, 3, and 4.