Question

How do you solve \[4x-\left( 2x+3 \right)=7\]?

Answer 1

Hint: In order to find the solution to the given question that is to solve the equation \[4x-\left( 2x+3 \right)=7\]to find the value of variable \[x\], we will apply the distributive property which is given by \[\text{A }\left( \text{ B}+\text{ C} \right)\text{ }=\text{ AB }+\text{ AC}\] where A, B and C are three different values. After this we will combine the like terms. Finally, we will simplify the expression to get the value of \[x\].

Complete step-by-step answer:
According to the question, given equation in the question is as follows:
\[4x-\left( 2x+3 \right)=7\]
first apply the distributive property which states that when a factor is multiplied by the sum/addition of two terms, it is essential to multiply each of the two numbers by the factor, and finally perform the addition operation. This property can be stated symbolically as: \[\text{A }\left( \text{ B}+\text{ C} \right)\text{ }=\text{ AB }+\text{ AC}\] where \[A=-1\], \[B=2x\] and \[C=3\] are three different values in the above equation, we get:
\[\Rightarrow 4x-2x-3=7\]
After this combine the like terms from the above equation where “term” is each part of the expression. Here the letter \[x\] is called a variable and since they all have the same variable \[x\] they are referred to as “like terms”, we get:
\[\Rightarrow 2x-3=7\]
Now, add \[3\] to both the side of the above equation, we get:
\[\Rightarrow 2x-3+3=7+3\]
Simplify the above equation by adding the numbers, we get:
\[\Rightarrow 2x=10\]
Divide \[2\] to both the sides of the above equation, we get:
\[\Rightarrow \dfrac{2x}{2}=\dfrac{10}{2}\]
After simplifying the above equation, we get:
\[\Rightarrow x=5\]
Therefore, after solving the given equation \[4x-\left( 2x+3 \right)=7\]we get \[x=5\].

Note: Students generally make mistakes while opening the brackets while simplifying such expressions. They basically ignore multiplying the sign of the terms which leads to the wrong answer. So, it’s important to remember that when we do multiplication or open the brackets, we also have to multiply the sign of the terms like “negative term multiply by negative term gives positive term” and “positive term multiply by negative term gives negative term”.