Question

Solve the following equation and check your answer: \[x + \left( {x + 2} \right) = \left( {x + 4} \right) + 31\].

Answer 1

Hint: In the given question, we have been given a linear equation in one variable. We have to solve for the value of the given variable. We can easily do that if we know the method to solve any linear equation in one variable. We can do that by taking the constants multiplied with the variable to the other side, so as to free the variable of any coefficient and then simplify the constants to get the value of the variable.

Complete step-by-step solution:
The given linear equation is \[x + \left( {x + 2} \right) = \left( {x + 4} \right) + 31\].
First, we are going to simplify the brackets,
\[x + x + 2 = x + 4 + 31 \Rightarrow 2x + 2 = x + 35\]
Now, we are going to take the like terms on different sides,
\[2x - x = 35 - 2\]
Hence, we have,
\[x = 33\]
Now, we are going to verify by putting the value of \[x\] in the original equation and if both sides are equal, our answer is correct, so, we have,
\[33 + \left( {33 + 2} \right) = \left( {33 + 4} \right) + 31\]
Solving the bracket and opening them,
\[33 + 35 = 37 + 31\]
Now, adding them up,
\[68 = 68\]
Hence, the calculated answer is correct.

Note: In the given question, we had to calculate the value of a linear equation in one variable. We did that by first solving the bracket by simplifying their value, multiplying the ones outside with the ones inside, taking the constant multiplied with the variable to the other side containing the other constant. Then we simply divided the constants and got our answer.