Question

The value x=4 is a solution to all of the following equations except which?1. 2x+7=152. 3(x+1)=x+113. x+5=3x-34. x+12=5x-2

Answer 1

Step-by-step explanation

How to know that x=4 is not a solution to an equation? To verify this, we just evaluate the equation for x=4, to obtain a contradiction.

Let's do this for the first equation:

`\begin{gathered} 2(4)+7=15, \\ 8+7=15, \\ 15=15. \end{gathered}`

Here, we didn't get a contradiction (15 is equal to itself). This means that x=4 is indeed a solution to this equation.

Let's test the second one:

`\begin{gathered} 3(4+1)=4+11, \\ 3\cdot5=15, \\ 15=15. \end{gathered}`

As before, we have that x=4 is a solution.

Let's test the third one:

`\begin{gathered} 4+5=3(4)-3, \\ 9=12-3, \\ 9=9. \end{gathered}`

Again, x=4 is a solution.

Finally, let's verify the last one:

`\begin{gathered} 4+12=5(4)-2, \\ 16=20-2, \\ 16=18. \end{gathered}`

We got a contradiction! 16 is not equal to 18.

Answer

The answer is the fourth option (equation).