Question

How many solutions exist for the equation: 8(4-2x)=4(3-5x)+4x

A) Two solutions
B) One solution
C) No solution
D) Many solutions

Answer 1

C

Explanation:

There are no values of x that make the equation true.

No solution

Answer 2

C

Explanation:

We have the equation:

`8(4-2x)=4(3-5x)+4x`

Let's expand both sides. Distribute on the left:

`32-16x=4(3-5x)+4x`

Distribute on the right:

`32-16x=12-20x+4x`

Combine like terms on the right:

`32-16x=12-16x`

Add 16x to both sides:

`32\\eq12`

This is not true.

So, our equation has no solutions.

This would mean that our two linear equations are parallel to each other.

Our answer is C