Why does this equation have no solution 3(x + 4) = 8x + 3 − 5x ?
Good question, let’s have a look!
3(x + 4) = 8x + 3  5x 3x + 12 = 3x + 3 {used distributive property on left side and combined like terms on right side} 12 = 3 {subtracted 3x from each side} = no solution Oh no, the variable disappeared! When solving an equation, and the variable is eliminated,  if you are left with a false statement, such as 12 = 3, there is no solution. {there is no value of x that makes the equation true}  if you are left with a true statement, such as 3 = 3, there are infinite solutions {any value of x would make the equation true} Ask the House
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