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

Last updated date: 09th Aug 2024
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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 $x = - 4.$