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Solve advanced linear equations

# Solve advanced linear equations

An equation is a mathematical statement that has an expression on the left side of the equals sign (=) with the same value as the expression on the right side.

One of the terms in an equation may not be know and needs to be determined. Often this unknown term is represented by a letter such as "x".

(e.g. 5 + x = - 2)

Solving
an equation means manipulating the expressions and finding the value of the unknown variables. In order to solve for the unknown variable, you must isolate the variable

To keep an equation equal, we must do exactly the same thing to each side of the equation. If we add (or subtract) a quantity from one side, we must add (or subtract) that same quantity from the other side.

Solve for x: 2x+5=21

Notice that 2 is "closest" to variable x, and 5 is "farthest" away. This simple observation allows us to decide which number to eliminate first. It is obviously +5 because it is farther between the two. The opposite of +5 is -5, so that means we will subtract both sides of the equation by 5.

2x+5-5=21-5
2x=16

Now it's time to get rid of the number closest or directly attached to x which is 2. Since +2 is multiplying the variable x, its opposite operation is to divide by 2.

$\fs2\;\frac{2x}{2}=\frac{16}{2}\;\;\Rightarrow\;x=8$

Solve for s:

-6 = -1 - s

Simplify your answer and write it as a proper fraction or as a whole or mixed number.

Solution: