If four 𝑥 plus nine 𝑥 plus three 𝑥 plus two 𝑥 equals one hundred and eight, what is the value of nine 𝑥 plus seven?
This means we should take our equation, solve for 𝑥, and once we have a value of 𝑥, we will use it to find the value of nine 𝑥 plus seven. So the first thing we need to do to solve for 𝑥, is we need to combine like terms on the left-hand side. Four 𝑥 plus nine 𝑥 plus three 𝑥 plus two 𝑥 is equal to eighteen 𝑥. And we set it equal to one hundred and eight. Now let’s go ahead and divide both sides by eighteen. On the left, the eighteens cancel. And on the right, one hundred and eight divided by eighteen is six, so 𝑥 equals six.
So now to find the value of nine 𝑥 plus seven, we will take 𝑥 and replace it with the value of six. So we have nine times six plus seven. Following the order of operations, we need to multiply nine and six before we add the seven. And nine times six is equal to fifty-four. And fifty-four plus seven is equal to sixty-one.
Since the value of 𝑥 is six, the value of nine 𝑥 plus seven is equal to sixty-one.