The width of a rectangle is w yards and the length of the rectangle is left parenthesis 7 w minus 4 right parenthesis yards. The perimeter of the rectangle is given by the algebraic expression 2wplus 2left parenthesis 7 w minus 4 right parenthesis. Simplify the algebraic expression 2wplus
2left parenthesis 7 w minus 4 right parenthesis and determine the perimeter of a rectangle whose width w is 3 yards.
Simplify the algebraic expression 2 w plus 2 left parenthesis 7 w minus 4 right parenthesis = ____
To simplify the expression 2w + 2(7w-4), we can begin by distributing the 2 to both terms inside the parentheses:
2w + 2(7w-4) = 2w + 14w - 8
Next, we can combine like terms by adding the coefficients of the w terms:
2w + 14w = 16w
So the simplified expression is:
16w - 8
To find the perimeter of a rectangle with a width of 3 yards, we substitute w = 3 into the simplified expression:
16(3) - 8 = 48 - 8 = 40
Therefore, the perimeter of the rectangle is 40 yards.
To simplify the algebraic expression 2w + 2(7w - 4), we can use the distributive property to remove the parentheses:
2w + 2(7w - 4) = 2w + 14w - 8
Now, we can combine like terms by adding the coefficients of w:
2w + 14w = 16w
Finally, the simplified expression is:
16w - 8
To determine the perimeter of a rectangle with a width of 3 yards, we can substitute w = 3 into the simplified expression:
Perimeter = 16w - 8
Perimeter = 16(3) - 8
Perimeter = 48 - 8
Perimeter = 40 yards