Question

How do you solve 2(x + 1) + 4 = 8?

Answer 1

Hint: We are asked to find the solution of 2(x + 1) + 4 = 8. First, we will learn what a linear equation in 1 variable term is and then we use the hit and trial method to find the value of ‘x’. In this method, we will put the value of ‘x’ one by one by hitting the arbitrary values and looking for the needed values. Another method is to apply algebra. We will subtract the terms to get to our final term and get our required solution. We also require the help of the BODMAS method to simplify our term with the bracket around.

Complete step-by-step solution:

We are given that we have 2(x + 1) + 4 = 8. We are asked to find the value of x or we are asked how we will be able to solve this expression. We will first learn about the equation in one variable. One variable simply represents the equation that has one variable (say x, y, or z) and another one constant. For example, x + 2 = 7 or 2 (x + 2) = 7, etc. Our equation 2(x + 1) + 4 = 8 also has just one variable ‘x’. We have to find the value of ‘x’ which will satisfy our given equation.
First, we will try by the method of hit and trial in which we will put a different value of ‘x’ and take which one fits the solution correctly.
Let, x = 0 in 2(x + 1) + 4 = 8. We get,
\[\Rightarrow 2\left( 0+1 \right)+4=8\]
\[\Rightarrow 2+4=8\]
\[\Rightarrow 6=8\]
which is not true. So, x = 0 is not the solution.
Let x = – 1 in 2(x + 1) + 4 = 8. We get,
\[\Rightarrow 2\left( -1+1 \right)+4=8\]
\[\Rightarrow 4=8\]
which is not true. So, x = – 1 is not the solution.
Putting x = – 2 in 2 (x + 1) + 4 = 8. We get,
\[\Rightarrow 2\left( -2+1 \right)+4=8\]
\[\Rightarrow -2+4=8\]
\[\Rightarrow 2=8\]
which is not true. So, x = – 2 is not the solution.
Putting x = 1 in 2 (x + 1) + 4 = 8. We get,
\[\Rightarrow 2\left( 1+1 \right)+4=8\]
\[\Rightarrow 2\times 2+4=8\]
\[\Rightarrow 4+4=8\]
\[\Rightarrow 8=8\]
which is true. So, x = 1 is the solution to our problem.
Another way to solve this is to use the algebraic operation, we use multiplication, division, the addition between the variables and constants to simplify and solve. We have,
\[2\left( x+1 \right)+4=8\]
Subtracting ‘4’ on both the sides, we get,
\[\Rightarrow 2\left( x+1 \right)+4-4=8-4\]
On simplifying, we get,
\[\Rightarrow 2\left( x+1 \right)=4\]
Dividing both the sides by 2, we get,
\[\Rightarrow x+1=2\]
Subtracting 1 on both the sides, we get,
\[\Rightarrow x+1-1=2-1\]
\[\Rightarrow x=1\]
So, x = 1 is the solution to this question.

Note: Remember that we cannot add the variable to the constant. Usual mistakes like this where one adds constants with variables usually happen. For example, 3x + 6 = 9x, here one added ‘6’ with 3 of x and made it 9x, this is wrong. We cannot add constants and variables at once. Only the same variables are added to each other. When we usually open the bracket, we always multiply the terms with each term of the bracket, that is, a (b + c) = ab + ac.