Question

If \[42 = 3\left( {x - 4} \right)\], what is the value of \[x\]?
A.4
B.10
C.18
D.20

Answer 1

Hint: Here we will first expand the equation by opening the bracket of the equation using distributive property of multiplication. Then we will simplify and solve the equation by using the basic operation of addition, multiplication and division to get the value of \[x\].

Complete step-by-step answer:
Given equation is \[42 = 3\left( {x - 4} \right)\].
First, we will open the brackets by multiplying the constant with the terms inside the brackets. That is we will use distributive property to simplify the equation. Therefore, we get
\[ \Rightarrow 42 = 3x - 3 \times 4\]
Now by multiplication of terms, we get
\[ \Rightarrow 42 = 3x - 12\]
Now we simplify this equation further by taking all the constant terms to the right side of the equation and terms with \[x\] to the left side of the equation. Therefore, we get
\[ \Rightarrow 3x = 42 + 12\]
Adding the terms, we get
\[ \Rightarrow 3x = 54\]
Dividing both the side by 3, we get
\[ \Rightarrow x = \dfrac{{54}}{3}\]
\[ \Rightarrow x = 18\]
Hence the value of \[x\] is equal to 18.
So, option C is the correct option.

Note: Here, we have used the distributive property of multiplication to simplify the equation. The distributive property states that when a term is multiplied to sum of two terms, then it is given by \[a \cdot \left( {b + c} \right) = ab + bc\]. In this question, the given equation is a linear equation with only one variable. Here, instead of multiplying 3 to the terms in the bracket, we can simply divide both sides by 3 and solve further to get the value of \[x\].
\[42 = 3\left( {x - 4} \right)\]
Dividing both side by 3, we get
\[ \Rightarrow \dfrac{{42}}{3} = x - 4\]
\[ \Rightarrow 14 = x - 4\]
Adding 4 on both sides, we get
\[\begin{array}{l} \Rightarrow 14 + 4 = x\\ \Rightarrow x = 18\end{array}\]