Question

does the equation 3(x + 6) = 3x + 18 have one solution, no solutions, or infinitely many solutions?
there are x terms on both sides of the equation, and were trying to isolate x. lets get rid of the x term from one of the sides. what move could we make to get rid of the 3x on the right side while keeping the equation balanced?
3(x + 6) = 3x + 18
3x + 18 = 3x + 18
multiply each side by 3x subtract 3x from each side
add 3x to each side

Explanation:

Step1: Analyze the goal

We need to eliminate the \(3x\) term from the right - hand side of the equation \(3x + 18=3x + 18\) while keeping the equation balanced. The principle of equation balancing states that we can perform the same operation on both sides of an equation.

Step2: Evaluate each option

• Option 1: Multiply each side by \(3x\). If we multiply both sides by \(3x\), the equation becomes \(3x(3x + 18)=3x(3x + 18)\), which is \(9x^{2}+54x = 9x^{2}+54x\). This does not eliminate the \(3x\) term from the right - hand side, it complicates the equation.
• Option 2: Subtract \(3x\) from each side. If we subtract \(3x\) from both sides of \(3x + 18=3x + 18\), we get \((3x + 18)-3x=(3x + 18)-3x\). Simplifying both sides, \(18 = 18\). This operation eliminates the \(3x\) term from both sides and keeps the equation balanced.
• Option 3: Add \(3x\) to each side. If we add \(3x\) to both sides of \(3x + 18=3x + 18\), we get \((3x + 18)+3x=(3x + 18)+3x\), which simplifies to \(6x+18 = 6x + 18\). This does not eliminate the \(3x\) term from the right - hand side, it adds more \(x\) terms.

Answer:

Subtract 3x from each side