Algebra - Linear Equations

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Section 2.2 : Linear Equations

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1. Solve the following equation and check your answer.

\[4x - 7\left( {2 - x} \right) = 3x + 2\]

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First, we need to clear out the parenthesis on the left side and then simplify the left side.

\[\begin{align*}4x - 7\left( {2 - x} \right) & = 3x + 2\\ 4x - 14 + 7x & = 3x + 2\\ 11x - 14 & = 3x + 2\end{align*}\] Show Step 2

Now we can subtract 3\(x\) and add 14 to both sides to get all the \(x\)’s on one side and the terms without an \(x\) on the other side.

\[\begin{align*}11x - 14 & = 3x + 2\\ 8x & = 16\end{align*}\] Show Step 3

Finally, all we need to do is divide both sides by the coefficient of the \(x\) (i.e. the 8) to get the solution of \(x = 2\).

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Now all we need to do is check our answer from Step 3 and verify that it is a solution to the equation. It is important when doing this step to verify by plugging the solution from Step 3 into the equation given in the problem statement.

Here is the verification work.

\[\begin{align*}4\left( 2 \right) - 7\left( {2 - 2} \right) & \mathop = \limits^? 3\left( 2 \right) + 2\\ 8 & = 8\hspace{0.5in}{\mbox{OK}}\end{align*}\]

So, we can see that our solution from Step 3 is in fact the solution to the equation.