Final answer:
The perimeter of the triangle with sides x, 7x+8, and 6x-3 is obtained by adding these lengths together and simplifying to get the expression 14x + 5, which is option (a).
Step-by-step explanation:
To find the perimeter of a triangle, you add the lengths of all the sides together. Given the sides of the triangle have lengths x, 7x + 8, and 6x - 3, we can express the perimeter P as:
P = x + (7x + 8) + (6x - 3)
To simplify the algebra, we combine like terms:
P = x + 7x + 6x + 8 - 3
P = (1x + 7x + 6x) + (8 - 3)
P = 14x + 5
Therefore, the simplified expression for the perimeter of the triangle is 14x + 5, which matches option (a).
It is always good practice to check the answer to see if it is reasonable. In this case, all terms have been correctly combined and the simplification is accurate.