Solve 17 minus five 𝑥 is equal to six.
In order to solve any linear equation like this, we need to calculate the value of 𝑥. That means that the left-hand side is equal to the right-hand side. In this case, we need to find a value for 𝑥 such that 17 minus five 𝑥 is equal to six. One way of solving the equation is using the balancing method. Whatever we do to one side of the equation, we must do to the other. In this case, we’ll begin by adding five 𝑥 to both sides. On the left-hand side, we’re just left with 17 as negative five 𝑥 plus five 𝑥 is equal to zero. On the right-hand side, we have six plus five 𝑥.
Our next step is to subtract six from both sides. 17 minus six is equal to 11. Subtracting six from the right-hand side leaves us with five 𝑥 as six minus six is equal to zero. Finally, we can divide both sides of the equation by five. 11 divided by five can be written as a fraction as eleven-fifths or 11 over five. We write it this way as five doesn’t divide exactly into 11. On the right-hand side, five 𝑥 divided by five is equal to 𝑥. Therefore, 𝑥 is equal to eleven-fifths.
We could convert this answer into a mixed fraction or a decimal. 11 divided by five is equal to two remainder one. This means that eleven-fifths is equivalent to or the same as two and one-fifth. This would also be an acceptable answer for this question. 11 over five or eleven-fifths is the same as 22 over 10 or twenty-two tenths. Remember, with fractions, whatever we do to the top, we must do to the bottom. We can multiply the numerator and denominator both by two. The line in a fraction means divide. And 22 divided by 10 is equal to 2.2. Dividing any number by 10 moves all the digits one place to the right. This means that 𝑥 is equal to eleven-fifths, two and one-fifth, or 2.2. Any of these three answers are correct.
We can check our answer by substituting any of these values back into the original equation. Let’s substitute 𝑥 equals eleven-fifths. Substituting in this value gives us 17 minus five multiplied by eleven-fifths is equal to six. When we multiply five by eleven-fifths, the fives cancel. So we are just left with minus or negative 11. 17 minus 11 is equal to six. So our answer was correct.