Section 2.2 : Linear Equations
1. Solve the following equation and check your answer.
\[4x - 7\left( {2 - x} \right) = 3x + 2\]Show All Steps Hide All Steps
Start SolutionFirst, 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 2Now 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 3Finally, all we need to do is divide both sides by the coefficient of the \(x\) (i.e. the 8) to get the solution of \(x = 2\).
Show Step 4Now 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.