Question

How do you solve the equation $4\left( 1-3x \right)=88$

Answer 1

Hint: Now we are given with a linear equation in one variable. To solve the equation we will first use distributive property and simplify the equation. Now we will arrange the terms such that we have all the constants and variable terms on opposite sides. Now we will divide the whole equation by the coefficient of x and hence find the value of x.

Complete step-by-step solution:
Now we know that the given equation is a linear equation in x.
We want to find the solution of the given equation. Hence we want to find the value of x for which the equation holds true.
Now to solve the linear equation we will first simplify the given equation.
Now we will open the brackets using distributive property. We know that according to distributive property we have $a\left( b+c \right)=ab+ac$ hence $4\left( 1-3x \right)=4-4\left( 3x \right)$
Hence we can write the equation as
$\Rightarrow 4-4\left( 3x \right)=88$
Now using associative property we know that $a\left( bc \right)=\left( ab \right)c$ hence we get,
$\begin{align}
  & \Rightarrow 4-\left( 4\times 3 \right)x=88 \\
 & \Rightarrow 4-12x=88 \\
\end{align}$
Now we will separate the constant and variable terms.
Hence we have
$\Rightarrow 4-88=12x$
Now on simplifying the equation we get,
$\begin{align}
  & \Rightarrow -84=12x \\
 & \Rightarrow 12x=-84 \\
\end{align}$
Now dividing the whole equation by 112 we get
$\Rightarrow x=-7$
Hence the solution to the given equation is x = - 7.

Note: Now note that we can also solve this problem without using a distributive method. First we will divide the equation by 4 hence we will get the equation as 1 – 3x = 22. Now again we will use the same method to simplify the equation and then to find the value of x.