How to Solve linear equations

This question was submitted by Nonhle

Remember that when you are solving for x in a linear equation (that means that x does not have any exponents) you need to take all the numbers to one side and all the x’s to the other side.

For example: Solve for x:

4x + 5 = 7 – 2(-2x – 5)

First multiply out the bracket on the right:

4x + 5 = 7 + 4x + 10 Remember that a negative times a negative is a positive.

when we take the x’s to the one side we notice that they cancel:

4x -4x + 5 = 17

This means that there is no real solution for x, or x does not exist. The two sides of the equation are not equal to each other.

If we changed the equation to say:

4x + 5 = 7 + 2(-2x – 5)

Then we could solve for x (Remember you cant change the equation in the exam – try to answer the question given to you. If the teacher realises that the question is wrong when she/he starts to mark it – you will get the marks anyway).

4x + 5 = 7 -4x – 10

4x + 4x = 7 – 10 -5 Take the x’s to one side and the numbers (or constants) to the other side.
8x = -8 Now divide both sides by the number attached to the x
x = -1 Now you have your final answer
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