Question

1. solve 49x + 9 = 49x + 83. a. does the equation have one solution, no solution, or infinitely many solutions? b. write two equations in one variable that have the same number of solutions as this equation.

Explanation:

Step1: Subtract 49x from both sides

\[49x + 9-49x=49x + 83-49x\]
\[9 = 83\]
Since the resulting statement is false, the equation has no solution.

Step2: Create two - no - solution equations

For an equation \(ax + b=ax + c\) where \(b
eq c\), it has no solution.
Equation 1: \(12x+5 = 12x + 10\)
Equation 2: \(25x+3=25x + 7\)

Answer:

a. No solution
b. \(12x + 5=12x + 10\), \(25x+3 = 25x + 7\)