Answer
Difference is that an algebraic expression, \[2\left( x-4 \right)+5x\]is the part of the equation\[2\left( x-4 \right)+5x=34\]. One must know first how to solve an algebraic expression given in the equation for solving that equation. Thus, the topic to solve an algebraic expression should be taught first than to solve an equation.
Work Step by Step
Consider an equation, \[2\left( x-4 \right)+5x=34\]and an algebraic expression,\[2\left( x-4 \right)+5x\].
There is difference between to solve an equation and to simplify an algebraic expression. An algebraic expression is part of the equation. This means that the set of an algebraic expression constitutes the equation with equal sign. As seen in this question, that an algebraic expression\[2\left( x-4 \right)+5x\]is part of the equation\[2\left( x-4 \right)+5x=34\]. Thus, first it is required to simplify the expression \[2\left( x-4 \right)+5x\]will provide proceeds in solving equation\[2\left( x-4 \right)+5x=34\]. When all expression is solved collect like terms one side and constants to another side. Solve it further and get the solution for the equation\[2\left( x-4 \right)+5x=34\].
So, simplify the expression\[2\left( x-4 \right)+5x\] as follows:
\[\begin{align}
& 2\left( x-4 \right)+5x=2x-8+5x \\
& =\left( 2x+5x \right)-8 \\
& =7x-8
\end{align}\]
This is simplified since further simplification is not possible in this expression.
Now, solve the equation\[2\left( x-4 \right)+5x=34\]provides:
\[\begin{align}
& 2\left( x-4 \right)+5x=34 \\
& 2x-8+5x=34 \\
& \left( 2x+5x \right)-8=34 \\
& 7x-8=34
\end{align}\]
Expression on the left-hand side is simplified but equation needs more simplification to get the solution.
So, add 8 to both sides of the equation as;
\[\begin{align}
& 7x-8=34 \\
& 7x-8+8=34+8 \\
& 7x=42
\end{align}\]
Divide both sides by 7;
\[\begin{align}
& 7x=42 \\
& \frac{1}{7}\left( 7x \right)=\frac{1}{7}\left( 42 \right) \\
& x=6
\end{align}\]
The solution set for equation is\[\left\{ 6 \right\}\].
Thus, it is clear that it is must to know first that how to solve the algebraic expression and then proceed to have the knowledge about how to solve the equation.
