Question

7 - 5 + 3x - 1 = __x + __Fill in the blanks to get an equation that has no solutions

Answer 1

An equation with no solutions, is whne no matter what the unknown is, it never will be true.

First, we can have the same unknown on both sides: 3x

And then we can solve the left hand side of the equation, adding all the numbers:

$\begin{gathered} \text{Left-hand side:} \\ 7-5+3x-1=3x+1 \end{gathered}$

Now, if we have the same 3x in the right:

$3x+1=3x+\text{\_\_}_{}$

We have to add in the right side of the equation a number different from 1. Let's take 2. Then we have:

$3x+1=3x+2$

And we can verify that this equation does not have any solutions, by substracting 3x on both sides, and we get:

$\begin{gathered} 3x-3x+1=3x-3x+2 \\ 1\ne2 \end{gathered}$

Which is never true, and thus the euqation does not have any solutions.