Question

does the equation 3(x + 6) = 3x + 18 have one solution, no solutions, or infinitely many solutions? you just performed balanced moves to try to isolate x, and found that 18 = 18. how many solutions does this equation have? 3(x + 6) = 3x + 18 3x + 18 = 3x + 18 - 3x - 3x 18 = 18 no solutions one solution infinitely many solutions

Explanation:

Step1: Analyze the equation simplification

After simplifying \( 3(x + 6)=3x + 18 \), we get \( 3x+18 = 3x + 18 \), and then subtracting \( 3x \) from both sides gives \( 18 = 18 \).

Step2: Determine the number of solutions

When an equation simplifies to a true statement (like \( 18 = 18 \)) that is always true, regardless of the value of \( x \), the equation has infinitely many solutions because any value of \( x \) will satisfy the original equation.

Answer:

Infinitely many solutions