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.

x - 3 = 3 - x

answer attempt 1 out of 2
the equation has select an option
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Explanation:

Step1: Solve the equation \( x - 3 = 3 - x \)

Add \( x \) to both sides: \( x + x - 3 = 3 - x + x \), which simplifies to \( 2x - 3 = 3 \).

Step2: Isolate the variable term

Add 3 to both sides: \( 2x - 3 + 3 = 3 + 3 \), so \( 2x = 6 \).

Step3: Solve for \( x \)

Divide both sides by 2: \( \frac{2x}{2} = \frac{6}{2} \), giving \( x = 3 \).
This shows the equation has one solution (\( x = 3 \)). Now, we can test another value (e.g., \( x = 0 \)):
For \( x = 0 \): Left side: \( 0 - 3 = -3 \); Right side: \( 3 - 0 = 3 \). Since \( -3
eq 3 \), \( x = 0 \) is not a solution.
For \( x = 3 \): Left side: \( 3 - 3 = 0 \); Right side: \( 3 - 3 = 0 \). So \( x = 3 \) is a solution. Another test value, say \( x = 4 \): Left side: \( 4 - 3 = 1 \); Right side: \( 3 - 4 = -1 \). \( 1
eq -1 \), so not a solution.

Answer:

The equation \( x - 3 = 3 - x \) has one solution. Two values: \( x = 3 \) (is a solution) and \( x = 0 \) (is not a solution) support this (one solution exists as only \( x = 3 \) satisfies the equation).