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

select an option
one solution
infinite solutions
no solutions

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 \( x = 3 \). Since we found a unique solution, the equation has one solution.

Step4: Test values

• For \( x = 3 \): Left side \( 3 - 3 = 0 \), Right side \( 3 - 3 = 0 \), so it works.
• For \( x = 4 \): Left side \( 4 - 3 = 1 \), Right side \( 3 - 4 = -1 \), not equal (but this just shows other values don't work, confirming one solution).

Answer:

The equation has one solution. Two values: \( x = 3 \) (satisfies) and \( x = 0 \) (Left: \( 0 - 3 = -3 \), Right: \( 3 - 0 = 3 \), not equal, showing only \( x = 3 \) works).