'If I think of a number, multiply it by 10 and then add 2 it is the same as if I multiply it by 7 and add 14. What number am I thinking of?
Puzzles like this one have been used before in the other 'Equations' activities, but this one is more complicated. The answer is not just a number but I have done something else to the original number. This type of puzzle can still be written as an equation, but now we have to use an x (or whatever letter we use to stand for the number) on each side of the equal sign. So, the equation for this puzzle looks like this:
10x + 2 = 7x + 14
This looks more complicated but it can still be solved using the 'balancing' method we have used before, we just have to add an extra step. The first step is to change it into an equation where the 'x' is only on one side. There are 10 x's on the left and 7 x's on the right. If I remove the 7 x's from the right there will be no x's there. But, remember whatever I do to the right I must do to the left as well. This is how we set it out:
Now, the equation is just the same as we have solved before so you should know what to do. We need to subtract 2 from both sides, then divide by 3.The full working looks like this.
Hope you're following this. Here's another one to help.
3x - 5 = 10 - 2x
Now this time you will notice on the right-hand side the 2x is subtracted from 10. So, what we do in this case is add 2 x's to both sides first. This will get rid of the -2x. Here is the full working:
The rule to remember with these equations is look for the side with the fewest x's on and take them from both sides. If the x has a '-' sign in front then add them on instead of taking them away. Does it make sense? Have a go at the questions and don't worry if you get them wrong, just look at the solution.