Why does this equation have no solution?

Why does this equation have no solution 3(x + 4) = 8x + 3 − 5x ?

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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