Question

sort each equation by the number of solutions it has.

• no solution

$7s + 3 = -3 + 7s$

• one solution

$5x = x + 8$

• infinitely many solutions

$10m - 5 = -5 + 10m$
$9x + 6 = 3(2 + 3x)$

$2y - 1 = 1 + 2y$

Explanation:

Step1: Analyze the equation \(2y - 1 = 1 + 2y\)

Subtract \(2y\) from both sides of the equation. We get \((2y - 2y)- 1=(1)+(2y - 2y)\), which simplifies to \(-1 = 1\).

Step2: Determine the number of solutions

Since \(-1 = 1\) is a false statement, this means the equation \(2y - 1 = 1 + 2y\) has no values of \(y\) that will satisfy it. So it should be placed in the "no solution" category.

Answer:

The equation \(2y - 1 = 1 + 2y\) belongs to the "no solution" group (the left - most box with the equation \(7s + 3=-3 + 7s\)).