Question

Solve: \[5x-2\left( 2x-7 \right)=2\left( 3x-1 \right)+\dfrac{7}{2}\]

Answer 1

Hint: Consider the linear equation then make the variables as subjects or take variables to one side and constant term to the other and hence find the value of variable ‘x’.

Complete step-by-step answer:
In the question we are given an equation which is, \[5x-2\left( 2x-7 \right)=2\left( 3x-1 \right)+\dfrac{7}{2}\] and we have to find the value of x.
Let a linear equation can be written in form of,
\[ax+b=0\]
Where a and b are real numbers and x is a variable. This form is sometimes called the standard form of linear equations. Please note that most linear equations will not start of this form. Also the variable may or may not be an x or please don’t get too locked into always seeing x there.
These points are very important and help very much while solving any linear type of equations they should be kept in mind.
So, the given linear equation is:
\[5x-2\left( 2x-7 \right)=2\left( 3x-1 \right)+\dfrac{7}{2}\]
Now we will expand by multiplying in the respective sides of equation so we get,
\[5x-4x+14=6x-2+\dfrac{7}{2}\]
Now on simplification we get,
\[x+14=6x+\dfrac{3}{2}\]
So on subtracting ‘6x’ to both the sides we get,
\[x-6x+14=6x+\dfrac{3}{2}-6x\]
Or, \[-5x+14=\dfrac{3}{2}\]
Now subtracting ‘14’ from both the sides we get,
\[-5x+14-14=\dfrac{3}{2}-14\]
Or, \[-5x=\dfrac{-25}{2}\]
Hence, the value of x is \[\dfrac{5}{2}\].

Note: Students while solving these linear equations should do calculations such that all the variables which need to be found out need to be on one side and the constants to be on another side such that the variable is the subject of the equation and hence solve it to get as were.
Now for solving linear equations we will make heavy use of facts which are,
(i) If a = b then a + c = b + c for any value of c. All this saying is that we can add a number c to both the sides of the equation and not change the equation.
(ii) If a = b then a – c = b – c for any value of c. All this saying is that we can subtract a number c to both the sides of the equation and not change the equation.
(iii)If a = b then ac = bc for any non-zero value of c, so that the value of the equation remains unaltered.
(iv) If a = b, then \[\dfrac{a}{c}=\dfrac{b}{c}\] for any non – zero value of c, so that the value of the equation remains unaltered.