Question

Which equation below would give you the answer no solution?

A. 3x + 3 = 3x + 3
B. 3x + 3 = 3x + 2
C. 3x + 3 = 0
D. 3x + 3 = 6x + 6

Answer 1

To find the equation that doesn't have any solutions, we are going to solve each equation.

The first one is
`\bf{3x+3=3x+3}`. Begin by subtracting 3x and 3 from both sides :

⇒
`\bf{3x-3x=3-3}`

⇒
`\bf{0=0}`

So, this one has infinite solutions. Let's solve the next one:

⇒
`\bf{3x+3=3x+2}`

Subtract 3x and 3 from both sides :

⇒
`\bf{3x-3x=2-3}`

⇒
`\bf{0x=-1}`

⇒
`\bf{0=-1}`

A false statement means no solutions.

The next one is :

⇒
`\bf{3x+3=0}`

Subtract 3 from both sides :

⇒
`\bf{3x=-3}`

Divide both sides by 3 :

⇒
`\bf{x=-1}`

This equation has one solution.

Let's solve the last one.

⇒
`\bf{3x+3=6x+6}`

Subtract 3x from both sides

⇒
`\bf{6x-3x+6=3}`

⇒
`\bf{3x+6=3}`

Subtract 6 from both sides

⇒
`\bf{3x=3-6}`

⇒
`\bf{3x=-3}`

⇒
`\bf{x=-1}`

So, the equation that has no solutions is 3x + 3 = 3x + 2.

Answer 2

The equation that would give you the answer "no solution" is:

B. 3x + 3 = 3x + 2

In this equation, if you subtract 3x from both sides:

3x + 3 - 3x = 3x + 2 - 3x

3 = 2

You end up with the statement "3 = 2," which is not true. This indicates that there is no solution to the equation, making it inconsistent.

Explanation: