Question

How do you solve \[7(2x + 5) = 4x - 9 - x\;?\]

Answer 1

Hint: We will multiply and subtract all the variables and constant terms separately and then we will calculate the value of \[x\]. On doing some calculation we get the required answer.

Formula used: If an equation contains a single variable in the following format, we can calculate the value of the variable in the following way.
Let's say, \[A(mx + n) = c\] is the given equation and we have to calculate the value of \[x\].
So, we can interpret the equation in following way:
\[ \Rightarrow Amx + An = c\].
Now, we can take the constant terms in R.H.S:
\[ \Rightarrow Amx = c - An\].
So, we can get the value of \[x\] by dividing the constant term by the coefficient of \[x\].
\[ \Rightarrow x = \dfrac{{c - An}}{{Am}}\].

Complete Step by Step Solution:
The given equation is \[7(2x + 5) = 4x - 9 - x\;.\]
Now, by subtracting the variables on the R.H.S, we get:
\[ \Rightarrow 7(2x + 5) = 3x - 9\].
Now, by doing the multiplication on L.H.S, we get:
\[ \Rightarrow 14x + 35 = 3x - 9.\]
Now, take the constant term on R.H.S and the variable term on L.H.S, we get:
\[ \Rightarrow 14x - 3x = - 35 - 9.\]
Now, perform the required operations on R.H.S and L.H.S, we get the following equation:
\[ \Rightarrow 11x = - 44.\]
Now, divide the constant term on L.H.S by the coefficient of\[x\] on R.H.S, we get:
\[ \Rightarrow x = \dfrac{{ - 44}}{{\;\;11}}.\]
Now, perform the division on R.H.S, we get:
\[ \Rightarrow x = - 4.\]

Therefore, the value of \[x\] or the solution of the equation is \[ - 4\].

Note: Alternate way to solution:
The given equation is\[7(2x + 5) = 4x - 9 - x\;.\]
We can divide both the sides of the equation by \[7\].
SO, by performing it, we get:
\[ \Rightarrow 2x + 5 = \dfrac{{4x - 9 - x}}{7}\].
Now, by solving on the R.H.S, we get:
\[ \Rightarrow 2x + 5 = \dfrac{{3x - 9}}{7}\].
Now, further splitting up the terms in R.H.S, we get:
\[ \Rightarrow 2x + 5 = \dfrac{{3x}}{7} - \dfrac{9}{7}\].
Now, taking the variable terms on L.H.S and constant terms on R.H.S, we get:
\[ \Rightarrow 2x - \dfrac{{3x}}{7} = - 5 - \dfrac{9}{7}\].
Now, by doing the subtractions on both the sides, we get:
\[ \Rightarrow \dfrac{{14x - 3x}}{7} = \dfrac{{ - 35 - 9}}{7}\].
Now, simplify it further:
\[ \Rightarrow \dfrac{{11x}}{7} = \dfrac{{ - 44}}{7}\].
Now, cancel out the same terms on the denominators, we get:
\[ \Rightarrow 11x = - 44.\]
By doing the division, we get:
\[ \Rightarrow x = \dfrac{{ - 44}}{{\;\;11}}\]
\[ \Rightarrow x = - 4.\]
\[\therefore \]The solution of the equation is \[x = - 4.\]