Question

Write and solve the equation that represents negative five times the absolute value of the quantity three plus four times t end quantity is equal to negative 115. equation: –5|3 4|(t) = –115; solution: t = 3.29 equation: –5(3) |4t| = –115; solution: t = –25 equation: |–5(3 4t)| = –115; solution: t = 4 and –4 equation: –5|3 4t| = –115; solution: t = 5 and –6.5

Answer 1

The correct equation is –5|3 + 4t| = –115, which yields the solutions t = 5 and t = –6.5. Depending on the context, the negative solution may be discarded, leaving t = 5 as the single valid solution.

Step-by-step explanation:

The equation that represents negative five times the absolute value of the quantity three plus four times t is equal to negative 115 can be written as –5|3 + 4t| = –115. To solve this, we first divide each side by –5 to get |3 + 4t| = 23. Since an absolute value equation can have two possible solutions, we have two equations to solve: 3 + 4t = 23 and 3 + 4t = –23.

For the first equation:

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• 4t = 20
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• t = 5

For the second equation:

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• 4t = –26
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• t = –6.5

The solutions are t = 5 and t = –6.5. However, if the context of the problem dictates that a negative value of t is not reasonable (for instance, if t represents time), then the solution t = –6.5 would be discarded, leaving the positive value t = 5 as the only valid solution.