# Linear Equations And Problem Solving $$\begin5x 5\color &=-3\color\ 5x &=-8\ \dfrac&=\dfrac\ x &= \dfrac \ &=\boxed\end$$ This was a tough one, so remember to check your answer and make sure no mistake was made.

$$\begin5x 5\color &=-3\color\ 5x &=-8\ \dfrac&=\dfrac\ x &= \dfrac \ &=\boxed\end$$ This was a tough one, so remember to check your answer and make sure no mistake was made.

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.

Let’s look at one more two-step example before we jump up in difficulty again.

Make sure that you understand each step shown and work through the problem as well.

It is easy to make a mistake here, so make sure that you distribute the number in front of the parentheses to all the terms inside.

## Linear Equations And Problem Solving

Solve: $$3(x 2)-1=x-3(x 1)$$ First, distribute the 3 and –3, and collect like terms.

$$\begin5w 2 &= 9\ 5w 2 \color &= 9 \color\ 5w &= 7\ \dfrac &=\dfrac\w=\boxed\end$$ The fraction on the right can’t be simplified, so that is our final answer. Then: $$\begin5w 2 &= 9\ 5\left(\dfrac\right) 2 &= 9\ 7 2 &= 9\ 9 &= 9 \end$$ So, we have the correct answer once again!

In the following examples, there are more variable terms and possibly some simplification that needs to take place.

In each case, the steps will be to first simplify both sides, then use what we have been doing to isolate the variable.

We will first take an in depth look at an example to see how this all works.

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