Final answer:
The correct equation that meets all the requirements (-5 as a coefficient for t, 7 as a constant, and a product of 11) is option (a): -5t + 7 = 11. This satisfies the equation when solved for t.
Step-by-step explanation:
To create an equation with the specific elements provided, we need to find the correct combination of the coefficient -5, the variable t, the constant 7, and the product 11. The equation options presented are:
- -5t + 7 = 11
- -5t = 7 + 11
- -5t - 7 = 11
- 7t - 5 = 11
To confirm the correct equation, we need to see which one, when solved for t, complies with having -5 as the coefficient of t, 7 as a constant, and results in the product 11. Let's rearrange each equation to find the correct answer:
(a) -5t + 7 = 11. Solve for t by subtracting 7 from both sides:
-5t = 11 - 7
-5t = 4
t = -4/(-5)
t = 4/5
(b) -5t = 7 + 11. Simplify the right side:
-5t = 18
t = 18/(-5)
t = -18/5
(c) -5t - 7 = 11. Solve for t by adding 7 to both sides:
-5t = 11 + 7
-5t = 18
t = 18/(-5)
t = -18/5
(d) This equation does not satisfy the requirement since -5 is not the coefficient of t.
The only equation that satisfies all the conditions (where the product of the coefficient and the variable, when added to the constant, equals 11) is option (a): -5t + 7 = 11.