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How do I solve linear equations?
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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 $x^{\prime} s$ to the other side.
For example: Solve for $\mathrm{x}$ :
$4 x+5=7-2(-2 x-5)$
First multiply out the bracket on the right:
$4 x+5=7+4 x+10$ 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:
$4 x-4 x+5=17$
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:
$4 x+5=7+2(-2 x-5)$
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).
$4 x+5=7-4 x-10$
$4 x+4 x=7-10-5 \quad$ Take the $x$ 's to one side and the numbers (or constants) to the other side.
$\begin{array}{ll}8 x=-8 & \text { Now divide both sides by the number attached to the } x \\ x=-1 & \text { Now you have your final answer }\end{array}$
by Diamond (59.2k points)

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