Question

Solve \[3.7 = - 3x + x - 30x\]?

Answer 1

Hint: We take $x$ commotion from right hand side and calculate the constant term along with it. Convert the decimal into fraction form and calculate the value of $x$.
Convert a decimal number into fraction by writing the number in numerator (without decimal point) and writing \[{10^n}\] in a denominator where \[n\] is the number of places where the decimal is placed (counting from right end).

Complete step by step solution:
Since the equation has only one variable i.e. x, we will calculate the value of x.
We are given the equation \[3.7 = - 3x + x - 30x\] which has only one variable i.e. x.
We take x common from right hand side of the equation
\[ \Rightarrow 3.7 = x( - 3 + 1 - 30)\]
Calculate the value in the bracket first by adding terms of same sign and then adding or subtracting
\[ \Rightarrow 3.7 = x( - 33 + 1)\]
\[ \Rightarrow 3.7 = - 32x\]
Now convert the left hand side of the equation from decimal form to fraction form. Since there is only 1 digit after the decimal, we write 10 in the denominator and 37 in the numerator
 \[ \Rightarrow \dfrac{{37}}{{10}} = - 32x\]
Divide both sides by -32
\[ \Rightarrow \dfrac{{37}}{{10 \times ( - 32)}} = \dfrac{{ - 32x}}{{ - 32}}\]
Cancel same factors from numerator and denominator on right hand side of the equation
\[ \Rightarrow \dfrac{{ - 37}}{{10 \times 32}} = x\]
Divide 37 by 32
\[ \Rightarrow \dfrac{{ - 1.15625}}{{10}} = x\]
Convert fraction to decimal by shifting the decimal to one side to the left
\[ \Rightarrow - 0.115625 = x\]
\[\therefore \] The solution of \[3.7 = - 3x + x - 30x\] is \[x = - 0.115625\].

Note: Make sure you don't leave the answer in fraction form, As we have the left hand side in decimal form so the final answer should be decimal too. Also, follow BODMAS rule. Keep in mind we always add first and then subtract the terms.