Question

How do you solve $4( - x + 4) = 12?$

Answer 1

Hint: Use the distributive property of multiplication to open the parentheses on the left hand side, then respectively send the variable terms to the left hand side and the constant terms to the right hand side of the equation with help of algebraic operations and finally divide both sides with the coefficient of variable to get the required solution.Distributive law of multiplication is given as following: $a(b + c) = ab + ac$.

Complete step by step answer:
To solve the given equation $4( - x + 4) = 12$, we will first simplify it by opening the parentheses with the help of distributive property of multiplication as follows
$4( - x + 4) = 12 \\
\Rightarrow 4 \times ( - x) + 4 \times 4 = 12 \\
\Rightarrow - 4x + 16 = 12 \\ $
Now subtracting $16$ from both sides in order to group the constants at right hand side, we will get,
$- 4x + 16 - 16 = 12 - 16 \\
\Rightarrow - 4x = - 4 $
Since there are negative signs on both sides of the equation, so we can cancel each other,
$4x = 4$
Now dividing $4$ which is the coefficient of the variable $x$ from both sides we will get,
$\dfrac{{4x}}{4} = \dfrac{4}{4} \\
\therefore x = 1 \\ $
Therefore the required solution of the equation $4( - x + 4) = 12$ is calculated as $x = 1$.

Note: You may have noted that whenever we have performed an algebraic operation, we either subtracted or divided it with both sides, so we have to do it with both sides to preserve the balance of the equation, and it is important to perform with both sides, otherwise the result would be wrong.In the Cartesian plane, graph of the given equation will be a parallel line to y-axis, because the equation is consist of only one variable $(x)$ and also have degree equals to one.