We will look at the process of solving literal equations for a particular variable ( x ).
A literal equation is usually categorized by a myraid of constants that are crucial to the process which is being modeled. We solve such equation in terms of a controlling variable ( that we can choose to alter our process ).
For the following literal equations ( x ) will be the subject of variability.
[tex]3\cdot(bx\text{ - 2ab ) = }b\cdot(x-7a)\text{ + 3ab}[/tex]Whenever we have algebraic expressions we always refer to the rule of ( PEMDAS ).
Step 1: Solve the Parenthesis
We will solve for all the parenthesis in the equation given and write down the result:
[tex]3bx\text{ - 6ab = bx - 7ab + 3ab }[/tex]Step 2: Highlight and combine the like terms
All like terms are classified on the basis of their constants ( a and b ) and variable ( x ) attached. We will highlight all the like terms and take simplify them on either side of the " = " sign:
[tex]\begin{gathered} 3bx\text{ }\text{\textcolor{#FF7968}{- 6ab}}\text{ = bx }\text{\textcolor{#FF7968}{-7ab}}\text{ }\text{\textcolor{#FF7968}{+ 3ab}} \\ 3bx\text{ - bx = 2ab} \end{gathered}[/tex]We combined three like terms ( -6ab , -7ab , and 3ab ).
Step 3: Factorize and simplify the equation
Now we will look for any constant that is present in all the terms throughout the equation. We see that constant ( b ) is common in all the terms. Hence, we will factor ( b ) out and cancel it out from each side of the " = " sign as follows:
[tex]\begin{gathered} b\cdot(3x\text{ - x ) = b}\cdot(2a) \\ \textcolor{#FF7968}{2x}\text{\textcolor{#FF7968}{ = 2a}} \end{gathered}[/tex]Step 4: Solve for the variable ( x )
We are left with a simple expression that relates the constant ( a ) and variable ( x ). We can go ahead and solve for the above:
[tex]\begin{gathered} x\text{ = }\frac{2a}{2} \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = a}} \end{gathered}[/tex]