When x=2 , the equation 3x−5 = 1 is true. Will any value of x make this equation true? Explain why or why not using examples to justify your answer.

No, x can only be 2.

Step-by-step explanation:

For this problem, we should solve the base equation for x to see if there is a singular value, or multiple values.  In order for this equation to have multiple values such that "any value of x makes this equation true", the equation must reduce to the form x = x.  Let's solve the equation for x:

3x - 5 = 1

3x - 5 + 5 = 1 + 5

3x = 6

3x * ( 1/3 ) = 6 * ( 1/3 )

x = 2

Note, the equation resolved to "x = 2".  This means that for the given equation, the only valid real solution is when x is 2.  No other value is valid.

In general, a good approximation of the number of real solutions to an equation can be determined by the order of the equation.  Note, since x is to the first power, this is a linear ( first-order) equation, meaning it will only have one real solution.

Cheers.