For their homecoming parade, the students of u-math have created a colorful banner, 41 meters in length, that is made of two pieces of parachute material. the short piece is 25 meters shorter than the long piece. find the length of each piece.
length of the long piece = ? m

33

Step-by-step explanation:

let the shorter piece be x m

then the longer piece is 41-x

"The short piece is 25 meters shorter then the long piece"

or

the difference between the longer and the shorter is 19

--->

(41-x) - x = 25

41-x-x = 25

-2x = 25-41

-2x = -16

divide both sides by -2

x = 8

I defined x to be the short piece 8

I defined 41-x to be the longer --- 41-8 = 33

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions