Here is the question. I have it solved but I'm not sure that my answer is right. Could someone please help?
A metal stays solid at Fahrenheit temperature below 1801.5 degrees. Determine ( in terms of an inequality) those Celsius temperatures for which the metal stays solid. Use the formula F=9/5C+32. The solution set is{C|C<__}.(Round to the nearest tenth.)
My answer is: (9/5)C+32<1801.5
(9/5)C<1801.5-32 (5/9)(9/5)C<(5/9)1769.5 C<983.06.
To determine the Celsius temperatures for which the metal stays solid, we need to use the given formula to convert the Fahrenheit temperature to Celsius.
The formula is: F = (9/5)C + 32, where F is the temperature in Fahrenheit and C is the temperature in Celsius.
Now, we want to find the Celsius temperatures for which the metal stays solid, meaning the Fahrenheit temperature should be below 1801.5 degrees.
We can rewrite the inequality as:
F < 1801.5
Substitute the formula for F:
(9/5)C + 32 < 1801.5
To isolate C, subtract 32 from both sides of the inequality:
(9/5)C < 1801.5 - 32
Simplify the right side:
(9/5)C < 1769.5
Now, multiply both sides of the inequality by (5/9) to solve for C:
(5/9)(9/5)C < (5/9)(1769.5)
Simplify:
C < (5/9)(1769.5)
Calculating this value, we get:
C < 983.06
Therefore, the solution set is:
{C | C < 983.06}
So, your answer of C < 983.06 is correct.