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

 Dec 12, 2023
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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≤−423​t+12

 

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

t2+423​t−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,∞)

 Dec 12, 2023

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