Question

1. sort each equation by the number of solutions it has.

no solution
one solution
infinitely many solutions
10m - 5 = -5 + 10m
9x + 6 = 3(2 + 3x)

Explanation:

Step1: Expand the right side

Expand \( 3(2 + 3x) \) using the distributive property \( a(b + c)=ab + ac \). So \( 3(2 + 3x)=3\times2+3\times3x = 6 + 9x \). The equation becomes \( 9x + 6=6 + 9x \).

Step2: Analyze the equation

Subtract \( 9x \) from both sides: \( 9x - 9x+6=6 + 9x - 9x \), which simplifies to \( 6 = 6 \). This is a true statement for all values of \( x \), so the equation has infinitely many solutions.

Answer:

The equation \( 9x + 6 = 3(2 + 3x) \) should be placed in the "infinitely many solutions" category.