Linear Equation Problem Solving

To solve linear equations, there is one main goal: isolate the variable. Therefore, to isolate $$x$$, you must divide that side by 4.In this lesson, we will look at how this is done through several examples. So we need to figure out how to isolate the variable. When doing this, you must remember one important rule: whatever you do to one side of the equation, you must do to the other side. $$\begin4x &= 8 \ \dfrac &= \dfrac\end$$ Simplifying: $$x = \boxed$$ That’s it, one step and we are done.

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In the following examples, there are more variable terms and possibly some simplification that needs to take place.This isn’t 100% necessary for every problem, but it is a good habit so we will do it for our equations.In this example, our original equation was $$4x = 8$$.Linear equations in one variable are equations where the variable has an exponent of 1, which is typically not shown (it is understood).An example would be something like $$12x = x – 5$$. By doing this, we will slowly be getting the variable by itself. Solve the equation: $$4x = 8$$ In this example, the 4 is multiplying the $$x$$.Solve: $$5w 2 = 9$$ As above, there are two operations: $$w$$ is being multiplied by 5 and then has 2 added to it.We will undo these by first subtracting 2 from both sides and then dividing by 5.In these next examples, you will see how to work with equations that have two steps instead.If there is more than one operation, it is important to remember the order of operations, PEMDAS.To “undo” this, we will add that value to both sides.Solve: $$y-9=21$$ This time, 9 is being subtracted from y. $$\beginy-9&=21\ y-9 \color&=21\color\y&=30\end$$ Next we will look at what are commonly called “two-step” equations.

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