Question

How do you solve $ - 4(3x + 2) = 16? $

Answer 1

Hint: First of all multiply the term outside the bracket with the terms inside the bracket. Then move all the constants on one side and the term with the variable on the opposite side. Then from the simplified equation, solve the equation for the resultant value for “x”

Complete step by step solution:
Take the given expression: $ - 4(3x + 2) = 16 $
Multiply the term outside the bracket with all the terms inside the bracket. When there is a negative sign outside the bracket then the sign of the terms inside the bracket also changes.
 $ - 12x - 8 = 16 $
Move constant from the left hand side of the equation to the right hand side of the equation. When any term is moved from one side of the equation to the opposite side then the sign of the term also changes. Negative terms become positive and vice-versa.
 $ - 12x = 16 + 8 $
Simplify the above equation the right hand side of the equation.
 $ - 12x = 24 $
Term multiplicative on one side of the equation when moved to the opposite side then goes to the denominator.
 $ x = - \dfrac{{24}}{{12}} $
Find the factors for the numerator of the term on the right hand side of the equation.
 $ x = - \dfrac{{12 \times 2}}{{12}} $
Common factors from the numerator and the denominator cancel each other. Therefore remove from the numerator and the denominator in the above equation.
 $ x = - 2 $
This is the required solution.
So, the correct answer is “ $ x = - 2 $ ”.

Note: Be careful about the sign convention while simplification. When you move any term from one side of the equation to the opposite side of the equation then the sign of the term also changes. Positive term becomes negative term and vice versa.