x2−x−4≤2
Subtract two from both sides to rewrite it in the quadratic standard form:
= x2−x−4−2≤2−2
= x2−x−6≤0
Now set it = 0 and factor and solve like normal.
= x2−x - 6=0
= (x−3)(x+2)=0 x + 2 = 0 or x - 3 = 0 x = -2 or x = 3
So the two zeros are -2 and 3, and will mark the boundaries of our answer interval. To find out if the interval is between -2 and 3, or on either side, we simply take a test point between -2 and 3 (for instance, x = 0) and evaluate the original inequality.
= x2−x−4≤2
= (0)2−(0)−4≤2
= 0−0−4≤2 −4≤2
Since the above is a true statement, we know that the solution interval is between -2 and 3, the same region where we picked our test point. Since the original inequality was less than or equal, we include the endpoints.
∴ −2≤x≤3.