Question

How do you solve 7x-7=2x+8 ?

Answer 1

Hint: In order to find the solution to the given question that is to solve the equation to find the value of variable \[x\], we will separate the variable \[x\] terms to one side and rest terms to the right-hand side. After combining the like terms, we will simplify the equation to get the value of \[x\].

Complete step-by-step solution:
According to the question, given equation in the question is as follows:
\[7x-7=2x+8\]
The method which is used to simplify such expressions is called “Collecting like terms”.
where “term” is each part of the expression. There are two terms in the given expression here namely \[7x\] and \[2x\].
Here the letter \[x\] is called a variable and since they all have the same variable \[x\] they are referred to as “like terms”. The number value in front of the variable is called the coefficient and includes the sign to simplify we add/subtract the coefficients.
To simplify the given equation, take the like terms to the left-hand side and rest in the right-hand side of the equation, we get:
\[\Rightarrow 7x-2x=8+7\]
To simplify this further, take the like terms in common and rest in bracket, we get:
\[\Rightarrow \left( 7-2 \right)x=8+7\]
Now, solve the terms with in the bracket with help of subtraction and solve the terms in the right-hand side of the equation with the help of addition, we get:
\[\Rightarrow 5x=15\]
Now, divide \[5\] from both of the sides we get:
\[\Rightarrow \dfrac{5x}{5}=\frac{15}{5}\]
Simplifying it further we get:
\[\Rightarrow x=3\]
Therefore, after solving the equation \[7x-7=2x+8\], we get \[x=3\]

Note: Students can go wrong if they are not aware of the concept of “Collecting Like terms” and meaning of it. It’s important to remember that the method which is used to simplify such expressions is called “Collecting like terms” 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”. The number value in front of the variable is called the coefficient and includes the sign to simplify we add/subtract the coefficients.