"I think of a number, multiply by 3 then add 7 and the answer is 19. What number am I thinking of?"
If you have completed the 'One-Step Equation' activity you will be familiar with problems like this. You will know that we can use a letter (usually x) for the unknown number then we can write the problem as an equation.
3x + 7 = 19
This equation is a bit more complex than before but we go about solving it in the same way. We think of an equation as a set of old fashioned weighing scales which balance.
If you add or take something from one side of the scales it will upset the balance unless you so the same thing to the other side. When we solve an equation we are trying to get the x by itself on the left-hand side. To do this we must first remove the +7 by doing the inverse which is -7. Then we must remove the 3 in front of the x remembering that this means 3 times x so the inverse is divide by 3. We set this out as follows:
So the solution to the equation is x = 4
Let's try another equation:
8x - 7 = 9
Remember the scales, what we do to one side of the equation, we must do to the other. Remember to do the inverse of -7 before the inverse of x8.
Remember x is not always used as the unknown, examiners could use any letter, but the principle is still the same!
Here's one more example.
20 - 3w = 8
Now, this is a little trickier as the 3w is subtracted from the 20, not the other way round. This is how we do it
Remember if you divide a negative by a negative you get a positive.
Now it's over to you. All the best!