Which equation has no solution?
.
.
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a) 4(x + 3) + 2x = 6 (x + 2)
b) 5 + 2(3 + 2x) = x + 3(x + 1)
c) 5(x + 3) + x = 4(x + 3) + 3
d) 4 + 6(2 + x) = 2(3x + 8)

B.

Step-by-step explanation:

If you simplify both sides and you have both sides in the form, , if the the number in front of the variable, is the same while the constant number, , is different then you will have no solutions.

If you have same and same , then you have infinitely many solutions.

If you have different then you have one solution.

Let's simplify both sides of A:

Distribute:

Combine like terms on left hand side:

The left hand side and right hand side have the same value no matter the x.  This has infinitely many solutions.

Let's simplify both sides of B:

Distribute:

Combine like terms on either side:

This is going to have no solutions.  If you thought about graphing y=4x+11 and y=4x+3 you would see that they are parallel and never cross.  

You could also try and solve it.

Subtract 4x on both sides:

11 is never 3.

11 isn't 3.

11=3 is not true which means there is no satisfying the equation labeled B.

Let's simplify both sides of C:

Distribute:

Combine like terms on either side:

This is going to have one solution.

We can solve it and see.

Subtract 4x on both sides:

Subtract 15 on both sides:

Divide both sides by 2:

0 is the one number that will make both sides the same for equation C.

Let's simplify both sides of D:

Distribute:

Combine like terms on left hand side:

These are the exact same expression on both sides and therefore will have the same value no matter the value of x you choose to plug in.

There are infinitely many solutions.