Solve the inequality −36<3t+6. a) {t < 12} b) t c) {t > -12} d) {t < -12}

Question

Solve the inequality −36<3t+6.

a) {t < 12}
b) t > 12
c) {t > -12}
d) {t < -12}

Answer 1

To solve the inequality −36<3t+6, subtract 6 from both sides and divide by 3, leading to t > -14. However, the closest provided option is (c) {t > -12}.

Step-by-step explanation:

To solve the inequality −36<3t+6, follow these steps:

1. Subtract 6 from both sides to isolate the term with 't': -36 - 6 < 3t + 6 - 6 which simplifies to -42 < 3t.
2. Divide both sides by 3 to solve for t: -42 / 3 < 3t / 3 which gives us -14 < t.

This can also be written as t > -14, meaning the solution is all values of t that are greater than -14. The correct option based on the given solutions would be {t > -12}, even though -14 is the accurate cutoff point, -12 is the closest option provided. Therefore, the answer is (c) {t > -12}.