Miss Williams tells her math class, “Five more than four times a number is more than 12.” Let 𝑥 represent the number and write an inequality that represents her statement.
If we start with the statement five more than four times a number is more than 12, and we want 𝑥 to represent the number, we’ll say, okay, this number is 𝑥. And we first want to know what’s happening to this number. Well, we have four times this number. So we can say four times 𝑥.
When we have the expression “more than,” we should ask, what is this five more than? It’s more than four times 𝑥. And that means we should take this four times 𝑥 and add five to it. But we then have another “more than” statement. This time, five more than four times a number is more than 12. This means everything that comes before is more than 12. Mathematically, we write that with a greater than symbol.
Now, we know that it’s more than 12, but it can’t be equal to 12. So we only have a greater than symbol, not a greater than or equal to. And then we bring down our 12. We simplify this by putting the four as the coefficient of 𝑥. Four 𝑥 plus five is greater than 12. Five more than four times a number is more than 12 can be written as four 𝑥 plus five is greater than 12.