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Given that \[5x - 2(6 + 7x) = 15\], the value of \[x\] is

Last updated date: 16th Jul 2024
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Hint: Solving for \[x\] in a linear equation we need to know some basic things.
While adding or subtracting integers of the same sign we will add their absolute value and put the same sign.
While adding the integers of different signs we will subtract their absolute value and put the greater number’s sign. Absolute value of an integer is nothing but the integer irrespective of their sign
In equations while transferring integers from one side to the other their sign will change. Also, if we do any operation on one side of the equation then we have to do the same on the other side too.

Complete step-by-step solution:
It is given that, \[5x - 2(6 + 7x) = 15\]
We have to simplify it so that we get all \[x\] terms on one side and the constant term other side.
 \[ \Rightarrow 5x - 12 - 14x = 15\]
Now let us add \[12\] on both sides of the equation,
 \[ \Rightarrow 5x - 12 - 14x + 12 = 15 + 12\]
On simplifying the above equation, we get
\[ \Rightarrow 5x - 14x = 27\]
Now we have achieved that all the \[x\] terms are in the left-hand side and the constant terms are in the right-hand side.
Let us simplify it further,
 \[ \Rightarrow - 9x = 27\]
Our aim is to find the value of \[x\] so, keep \[x\] alone on one side and take its coefficient to the other side.
 \[ \Rightarrow x = \dfrac{{27}}{{ - 9}}\]
Simplifying further we get,
   \[x = - 3\]
Therefore, the value of \[x\] is \[ - 3\]

Note: Absolute value of an integer is nothing but the integer irrespective of their sign. For instance, \[ - a\] and \[b\] be any integers then their absolute values are \[a\] and \[b\] respectively. Solving for \[x\] can also be done by the trial-and-error method but it takes time to find the correct value for \[x\] so we have used this method to solve.