Write an expression in simplified form for the perimeter of a pentagon. The sides measure 3x, 6x-2, x+3, 4x+1, and 5x-2.

To solve this question, you simply apply algebraic formulas to geometric relationships.

The perimeter is simply the sum of the lengths of the sides of a shape. However, in this case, there is an "x" involved, so you must add algebraically.

Simply add the length of the sides up.

[3x] + [6x-2] + [x+3] + [4x+1] + [5x-2] = Perimeter

Now, simplify. Since adding is commutative, you can simply put all the variables first and constants next, no matter where they come from within the expression.

3x + 6x + x + 4x + 5x + -2 + 3 + 1 + -2

19x + 0 (-2-2 + 3+1 cancel out)

The perimeter of this pentagon is 19x.

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