Question

question
determine whether the equation below has one solution, no solutions, or an infinite number of solutions. afterwards, determine two values of x that support your conclusion.
equation: ( x = x + 1 )
answer
the equation has (\boldsymbol{\text{no solutions}}).
a value of ( x ) that makes the equation false is (square). when substituted into the equation and fully evaluated, it turns the equation into (square = square).
another value of ( x ) that makes the equation false is (square). when substituted into the equation and fully evaluated, it turns the equation into (square = square).

Explanation:

Step1: Analyze the equation \(x = x + 1\)

Subtract \(x\) from both sides of the equation. We get \(x - x=x + 1-x\), which simplifies to \(0 = 1\). This is a contradiction, meaning the equation has no solutions.

Step2: Test with \(x = 0\)

Substitute \(x = 0\) into the equation \(x=x + 1\). The left - hand side (LHS) is \(0\), and the right - hand side (RHS) is \(0 + 1=1\). So, \(0=1\) which is false.

Step3: Test with \(x = 5\)

Substitute \(x = 5\) into the equation \(x=x + 1\). The LHS is \(5\), and the RHS is \(5+1 = 6\). So, \(5 = 6\) which is false.

Answer:

The equation has no solutions.
A value of \(x\) that makes the equation false is \(0\). When substituted into the equation and fully evaluated, it turns into \(0=1\).
Another value of \(x\) that makes the equation false is \(5\). When substituted into the equation and fully evaluated, it turns into \(5 = 6\).