Question

Jubal wrote the four equations below. He examined them, without solving them, to determine which equation has no solution. 7 x + 1 = 7 x+ 1. 3 x + 2 = 3 x minus 2. 4 x + 1 = 3 x + 8. negative 2 x minus 1 = negative 2 x minus 1. Which of Jubal’s equations has no solution?

Answer 1

Step-by-step explanation:

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Answer 2

Answer: The equation 3x + 2 = 3x - 2 has no solutions.

Step-by-step explanation:

So far, we know that we have four equations, and we have to find one that has no solutions. We can first examine them like Jubal did:

7x + 1 = 7x+ 1

3x + 2 = 3x - 2

4x + 1 = 3x + 8

-2x + 1 = -2x + 1

Just by looking at this, we see here that two of these equations look exactly the same even on the other side of the equation sign:

7x + 1 is the same as 7x + 1       AND

-2x + 1 is the same as -2x + 1

So we know that these are identities, meaning, they have infinitely many solutions. So, they cannot have no solutions because they are the ultimate opposite of that.

Next, looking at the other problems, we see that:

4x + 1 = 3x + 8       AND

3x + 2 = 3x - 2

Let's just take a look at the second equation from this selection. We see that this equation looks almost exactly the same on both sides of the equation sign, EXCEPT that the constants are different ( I mean 2 and -2 ). IF we WERE to add/subtract two from both sides, they wouldn't cancel out but instead leave you with 4. If you had subtracted the 3xs, then you would have been left with 0. So, 0 does NOT equal 6, so therefore, this has no solutions.

And what about 4x + 1 = 3x + 8?

If you just take a look at it, it only has one solution.

Hence, 3x + 2 = 3x - 2 has no solutions.