Question

How do you solve\[0.5=4.1x-2\left( 1.3x-4 \right)\]?

Answer 1

Hint: We can solve this question using basic linear equation concepts. First we have to multiply the terms in the parenthesis. Next we have to combine the like terms. After that we arrange the variable containing terms on one side and others on the other side. Now by applying some simplification techniques we will arrive at the solution.

Complete step by step answer:
Given equation is \[0.5=4.1x-2\left( 1.3x-4 \right)\]
First we have to multiply the terms in parenthesis
Then the equation will look like
\[\Rightarrow 0.5=4.1x-\left( 2.6x-8 \right)\]
Now we can remove the parentheses from the equation
\[\Rightarrow 0.5=4.1x-2.6x+8\]
Now we have to combine the like terms in the equation. So we have to subtract \[4.1x\] from \[2.6x\].
Then we will get the equation like
\[\Rightarrow 0.5=1.5x+8\]
To make like together we have to subtract 8 from both sides of the equation.
Then we will get
\[\Rightarrow 0.5-8=1.5x+8-8\]
By simplifying it we will get
\[\Rightarrow 0.5-8=1.5x\]
Now we have perform subtraction on LHS side then we will get
\[\Rightarrow -7.5=1.5x\]
Now we can rearrange our equation for our better understanding. For this we have to interchange our LHS with RHS and vice versa.
Then we will get
\[\Rightarrow 1.5x=-7.5\]
Now to find the value of \[x\] we have to simplify the above equation.
Now we have to divide the equation with \[1.5\] on both sides of the equation.
 Then we will get
\[\Rightarrow \dfrac{1.5x}{1.5}=-\dfrac{7.5}{1.5}\]
By simplifying it we will get
\[\Rightarrow x=-5\]
 So by simplifying the equation \[0.5=4.1x-2\left( 1.3x-4 \right)\] we will get the value of \[x\] as \[-5\].
 \[x=-5\]

Note: We can check the solution by substituting the \[x\] value in the equation then the equation has to be satisfied. We can also do it by making all the decimals numbers by multiplying and dividing by 10 and making into fractions. We can choose any method we are comfortable with.