Solve the inequality $4t^2 \le -9t + 12 - 14t + 36.$ Write your answer in interval notation.

blackpanther Dec 12, 2023

#1**0 **

Combining like terms on the right side of the inequality, we get:

4t2≤−23t+48

Dividing both sides by 4, we can write the inequality as:

t2≤−423t+12

Moving the constant term to the right side, we get:

t2+423t−12≤0

The left side of this inequality factors as:

(t−3)(t+4)≤0

This means that either (t−3)≤0 and (t+4)≤0, or (t−3)≥0 and (t+4)≥0. Solving these inequalities, we get:

t≤3 or t≥−4

Combining these two solutions using "or" logic, we get the interval solution:

t∈(−∞,−4]∪[3,∞)

BuiIderBoi Dec 12, 2023