Final answer:
To find the width of a rectangle given its length and perimeter, we can use the formula for the perimeter of a rectangle. By substituting the given values into the formula and simplifying the equation, we can isolate the width term and solve for it. In this case, the width of the rectangle is 2x + 5.
Step-by-step explanation:
To find the width of the rectangle, we need to use the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
Given that the perimeter of the rectangle is 10x + 18 and the length is 3x + 4, we can substitute these values into the formula: 10x + 18 = 2(3x + 4) + 2w.
Simplifying the equation, we get 10x + 18 = 6x + 8 + 2w. By combining like terms, we can isolate the width term: 2w = 10x + 18 - 6x - 8. Substituting in the given values, we have 2w = 4x + 10. Finally, divide by 2 to solve for w, giving us the width of the rectangle as 2x + 5.
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