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Solve the equation 4x + 2 = -5x + 20

Algebra is the enemy of many a student, but I'm here to show you that this (and many more concepts in maths!) really aren't that bad. 

For this problem, we need to group all of the like terms together, that is terms in the equation that take the same form, or look like each other. 

In this example, we have 4x on one side, and -5x on the other side. These can be simplified by, say, adding 5x to both sides. You can do this in maths, so long as you do the same thing to both sides. 

We see that if we add 5x to both sides, we get 9x on the left hand side (lhs) of the equals, and 0x on the right hand side (rhs) of the equals. Anything times 0 is 0, so 0x disappears from the rhs of the equation.

We're left with 9x + 2 = 20. Now we simplify further, by getting all the 'x' terms on one side, and all the numbers on the other. We can do this in the same way as before by subtracting 2 from both sides, to get 9x = 18. 

Now, we know that '9 times x' equals '18', but we want to know what 1 x is. To do this, we can divide both sides by 9. Doing this gives '9/9 times x' on the lhs and '18/9' on the rhs. Knowing that 9/9 = 1 and 18/9 is 2, we can see here that the solution simplifies to:

x = 2

Which is the answer. Learn the answer to this and more with me!  

Ben J. A Level Maths tutor, GCSE Maths tutor, 13 Plus  Maths tutor, I...

6 months ago

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