Each face of a cube has the numbers one to six, where the opposite sides add up to seven. Find the possible values of 𝑥.
The question tells us that each face of the cube has the numbers one to six. The question also tells us that opposite sides add up to seven. This means that 𝑥 plus 𝑥 equals seven. We need to find the two possible missing numbers which, added together, total seven.
We know that 𝑥 is not five because five is already given. What do we add to five to total seven? Five plus two equals seven. So these two numbers can be ruled out as possible values of 𝑥. Number three is also shown on the cube. We can rule out number three. But what do we add to three to make seven? Three plus four equals seven. So we can rule out number three and number four.
That means that number one could be 𝑥 and so could number six. So the possible values of 𝑥 are one and six.