Question

$4+5x=3x+1+2x$
Which of the following best describes the solution set to the equation shown above?

• A. The equation has exactly one solution, $x=0$
• B. The equation has exactly one solution, $x=1$
• C. The equation has no solution
• D. The equation has infinitely many solutions

Answer 1

The correct option is C The equation has no solution

A solution to an equation is a value of the variable (in this case $x$ ) that makes the equation true. Let's combine like terms:
$4+5x=3x+1+2x$
$4+5x=5x+1$
The two sides of the equation look similar, however, no matter what value of $x$ we substitute into the equation, we will get 4 = 1, which is not true. Therefore, the equation has no solution.