For the equation 2(4+x)+(13+x)=3x+k which value of k will create an equation with no solutions. a. x b. 3x .c 15 d. 21

Simplify the left side to get

2(4+x)+(13+x)

2(4)+2(x) +13+x

8+2x+13+x

3x+21

So the original equation

2(4+x)+(13+x) = 3x+k

turns into

3x+21 = 3x+k

Subtract 3x from both sides

3x+21 = 3x+k

3x+21-3x = 3x+k-3x

21 = k

k = 21

If k = 21, then the original equation will have infinitely many solutions. This is because we will end up with 3x+21 on both sides, leading to 0 = 0 after getting everything to one side. This is a true equation no matter what x happens to be.

If k is some fixed number other than 21, then there will be no solutions. This equation is inconsistent (one side says one thing, the other side says something different). If k = 15, then

3x+21 = 3x+k

3x+21 = 3x+15

21 = 15 subtract 3x from both sides

The last equation is false, so there are no solutions here.

note: if you replace k with a variable term, then there will be exactly one solution.

water molecules will move from the side of higher water concentration to the side of lower concentration until both solutions are isotonic. at this point, equilibrium is reached. in an isotonic solution, the flow of water in and out of the cell is happening at the same rate.

hope this < 3