Question

How do you solve \[9 + \dfrac{3}{4}x = \dfrac{7}{8}x - 10?\]

Answer 1

Hint: In this question we have to find the $x$ value from the above algebraic equation. For that we are going to simplify the equation. Next, we rearrange the variables and numbers. And also we are going to add and subtraction in complete step by step solution.
Here, Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols. In elementary algebra, those symbols represent quantities without fixed values, known as variables. The letters $x$ and $y$ represent the areas of the field.

Complete step-by-step solution:
To find the $x$ value:
Given,
\[ \Rightarrow 9 + \dfrac{3}{4}x = \dfrac{7}{8}x - 10\]
First, multiply through by their LCM in the above algebraic equation and we get
\[ \Rightarrow 4 = 2 \times 2\]
\[ \Rightarrow 8 = 2 \times 2 \times 2\]
\[LCM = 2 \times 2 \times 2\]
The LCM\[ = 8\].
Therefore,
\[ \Rightarrow 8(9) + 8\left( {\dfrac{3}{4}x} \right) = 8\left( {\dfrac{7}{8}x} \right) - 8(10)\]
Next, divide the coefficient of $x$ terms in the above equation and we get
\[ \Rightarrow 8(9) + {\not{8}^2}\left( {\dfrac{3}{{\not{4}}}x} \right) = \not{8}\left( {\dfrac{7}{{\not{8}}}x} \right) - 8(10)\]
\[ \Rightarrow 8(9) + 2\left( {3x} \right) = \left( {7x} \right) - 8(10)\]
Now, multiply the parenthesis on both sides and we get
\[ \Rightarrow 72 + 6x = 7x - 80\]
Then, we rearrange the numbers and variables on both sides and we get
\[ \Rightarrow 6x - 7x = - 80 - 72\]
Next, we subtract the left hand side (LHS) and adding the right hand side (RHS) and we get
\[ \Rightarrow - x = - 152\]
We cancel the minus sign on side and we get the required answer:
\[ \Rightarrow x = 152\]

Therefore the value of x is equal to 152.

Note: The students remember only the basics of the algebra equation. The basic of algebra equation is nothing but the simple operation of mathematics like addition, subtraction, multiplication, and division involving both constant as well as variable. For example, $x + 10 = 0$.
There is another little hard way to find the answer.
Given,
\[ \Rightarrow 9 + \dfrac{3}{4}x = \dfrac{7}{8}x - 10\]
First, move the all terms in left hand side and we get
\[ \Rightarrow \left( {\dfrac{3}{4}} \right)x - \left( {\dfrac{7}{8}} \right)x + 9 + 10{\text{ }} = {\text{ }}0\]
Next, combine the coefficient of $x$ in the above equation and find the LCM of the terms
\[ \Rightarrow \left( {\dfrac{3}{4} - \dfrac{7}{8}} \right)x + 9 + 10{\text{ }} = {\text{ }}0\]
\[ \Rightarrow \left( {\dfrac{{6 - 7}}{8}} \right)x + 9 + 10{\text{ }} = {\text{ }}0\]
Now, subtract and adding the above equation and we get
\[ \Rightarrow \left( {\dfrac{{ - 1}}{8}} \right)x + 19{\text{ }} = {\text{ }}0\]
\[ \Rightarrow \left( {\dfrac{{ - 1}}{8}} \right)x{\text{ = - 19}}\]
Then, move coefficient of $x$ in right hand side and we get
\[ \Rightarrow - x{\text{ = - 19}} \times {\text{8}}\]
\[ \Rightarrow - x = - 152\]
We cancel the minus sign on side and we get the required answer:
\[ \Rightarrow x = 152\]
This is the required answer for the given algebraic equation.
The purpose of algebra is to make it easy to state a mathematical relationship and its equation by using letters of the alphabet or other symbols to represent entities as a form of shorthand. Algebra then allows you to substitute values in order to solve the equations for the unknown quantities.
The main goal of algebra is to develop fluency in working with linear equations. Students will extend their experiences with tables, graphs, and equations and solve linear equations and inequalities and systems of linear equations and inequalities.