Solve three 𝑥 is equal to 9.6.
Solving an equation in this case for 𝑥 means to find the value of 𝑥 for which this statement is true. In order to do this, we apply a series of inverse operations. Remember inverse just means opposite. To help us decide which inverse operations to apply, let’s look at what’s happened to the 𝑥.
Three 𝑥 means three times 𝑥. So when 𝑥 is multiplied by three, we get a value of 9.6. To solve this equation then, we’ll need to perform the inverse operation. The opposite of multiplying by three is dividing by three. Remember we always apply these operations to both sides of the equation to make sure the equation is always balanced.
You might sometimes see this written as a fraction. Here, three 𝑥 over three is equal to 9.6 over three. That’s exactly the same as saying three 𝑥 divided by three is equal to 9.6 divided by three. Treating it like a fraction can make it easier to see what’s going on: three 𝑥 divided by three is simply 𝑥. We can see that as a fraction, we can simplify it by dividing both the numerator and the denominator by three.
So we just need to work out 9.6 divided by three now. When dividing a decimal number by an integer, that’s a whole number, we can use the bus stop method. We do need to remember though to add a decimal point directly above the decimal point in the number 9.6. Nine divided by three is three and six divided by three is two. That means then 9.6 divided by three is 3.2. 𝑥 is equal to 3.2.
It’s always good practice to check any answers we get by substituting them back into the original equation. In this case, if 𝑥 is equal to 3.2, three 𝑥 becomes three multiplied by 3.2. One way of doing this is to use the column method; though, any formal written method for multiplication is fine.
Since we’re multiplying a decimal number by an integer, we can add a decimal point in the same position in the answer for the column method. Two multiplied by three is six and three multiplied by three is nine. Since this gives us an answer of 9.6, we know that we’ve solved our equation correctly. 𝑥 is equal to 3.2.