Question

How do you solve $ - 2(2x + 5) - 3 = - 3(x - 1)$?

Answer 1

Hint:In this question we have to solve for the value of $x$ from the given linear equation of one variable. To solve the linear equation of one variable, we will first move all variables term to one side of the equation and all constant terms of the equation to the other side of the equation by performing necessary operations.

Complete step by step solution:
Let us try to solve this question in which we have to find the value of $x$ in the given equation. This is a linear equation in one variable. We will use BODMAS to simplify this equation$ - 2(2x + 5) - 3 = - 3(x - 1)$. In this equation, we have to simplify R.H.S and L.H.S both of the given linear equations.

To simplify this given linear equation we open brackets of L.H.S and multiply with $ - 2$.

Similarly we open brackets of R.H.S and multiply $ - 3$. After simplification we get,
$
- 2(2x + 5) - 3 = - 3(x - 1) \\
( - 2) \cdot 2x + ( - 2) \cdot 5 - 3 = ( - 3) \cdot x - ( - 3) \cdot 1 \\
- 4x - 10 - 3 = - 3x + 3 \\
$
Now, we will move all terms of variable $x$ to the L.H.S and constant terms to the R.H.S. So
we have after reorganization of terms,
$ - 4x + 3x = 10 + 3 + 3$

Here $ - 3x, - 10, - 3$ becomes $3x,10,3$ because when moving any from one side of the equation to the other side their signs will be changed.

So our equation becomes,
$
- 4x + 3x = 10 + 3 + 3 \\
- x = 16 \\
$
After multiplying value $ - x$ with $ - 1$, we get the value of $x$
$
( - x) \cdot ( - 1) = ( - 1) \cdot 16 \\
x = 16 \\
$
Hence the value of $x$ for the equation $ - 2(2x + 5) - 3 = - 3(x - 1)$ is $ - 16$.

We can also check whether our solution is correct or not by putting the value of $x$ in the equation $ -
2(2x + 5) - 3 = - 3(x - 1)$.
Putting value of $x = - 16$, we get
$
- 2(2x + 5) - 3 = - 3(x - 1) \\
- 2(2( - 16) + 5) - 3 = - 3( - 16 - 1) \\
- 2( - 32 + 5) - 3 = - 3( - 17) \\
- 2( - 27) - 3 = - 3( - 17) \\
54 - 3 = 51 \\
51 = 51 \\
$
Since $L.H.S = R.H.S$. Our Solution is correct.

Note: The questions in which we are given a linear equation in one variable and we have to solve for the value of the variable very easily. While solving for a linear equation in one variable you just have to be clear about the sign of constant and variable terms where most students make mistakes.