Question

How do you simplify $0.2\left( x+3 \right)-4\left( 2x-3 \right)=3.4$ ?

Answer 1

Hint: We can see there is only one unknown and one equation in the above question. So the equation is a linear equation in one variable, we can bring the variable to one side and constant to another side. Then divide both LHS and RHS by the coefficient of x to find the unknown.

Complete step-by-step answer:
The equation given in the question is $0.2\left( x+3 \right)-4\left( 2x-3 \right)=3.4$ which is a linear equation
Further solving it we get $0.2x+0.6+12-8x=3.4$
Let bring the variable to LHS and constant to RHS
We can subtract 12.6 from both LHS and RHS
So subtracting 12.6 from both sides we get - 7.8x = - -9.2
The coefficient of x is – 7.8, so dividing LHS and RHS by – 7.8
$\Rightarrow x=\dfrac{9.2}{7.8}=\dfrac{46}{39}$

Note: We know that the given equation is a linear equation which has only one unknown variable, but if a linear equation has n unknown variables, then we will need at least an equation to find the value of all variables. If we have less equations than variables there will be an infinite number of solutions for the system. We can solve this question by another method that is by graphical method we can draw the graph of y = -7.8x + 12.6 and y = 3.4 , and we can check the intersection point that will be our solution. In this case both the equations are of straight line so there will be one intersection point.