Question

how many solutions does this equation have?
$r + 2 + 19r = 2 + 20r$
no solution
one solution
infinitely many solutions

Explanation:

Step1: Combine like terms on left

$r + 19r + 2 = 2 + 20r$
$20r + 2 = 2 + 20r$

Step2: Subtract $20r$ from both sides

$20r - 20r + 2 = 2 + 20r - 20r$
$2 = 2$

Step3: Analyze the resulting equation

The equation simplifies to a true statement ($2=2$) that does not depend on the value of $r$, meaning all real numbers satisfy the original equation.

Answer:

infinitely many solutions