Final answer:
The value of 3x for a rectangle with a length of x+7, a width of 2x-3, and a perimeter of 32 is 12, which corresponds to option B.
Step-by-step explanation:
The question asks to find the value of 3x for a rectangle with given dimensions and perimeter. The dimensions of the rectangle are length x + 7 and width 2x - 3, with a perimeter of 32.
The perimeter (P) of a rectangle is calculated using the formula P = 2l + 2w, where l is the length and w is the width.
By substituting the given dimensions into the perimeter formula, we get:
32 = 2(x + 7) + 2(2x - 3). Simplifying this, we get:
32 = 2x + 14 + 4x - 6.
Combining like terms, we get:
32 = 6x + 8. Subtracting 8 from both sides gives us:
24 = 6x. Dividing both sides by 6 gives us the value of x, which is 4.
Finally, to find the value of 3x, we simply multiply 3 by 4, giving us an answer of 12, which corresponds with option B in the provided choices.