Question

How do you simplify $2x - (3 - 4x) + 2(x + 5)?$

Answer 1

Hint: As we know that a linear equation is an algebraic equation of the form $y = mx + b$, involving only a constant and a first order (linear) term, where $m$is the slope and $b$is the $y$-intercept. These have the order equal to unity or one. The linear equation in one variable is written in standard form as $ax + b = 0$i.e. only one variable. It is classified into different types based on the number of variables like linear equations in one variable or linear equations in two variables.

Complete step-by-step solution:
The equation of a straight line can be written in several forms. $y = mx + b$ is one of the forms of linear equations in one variable. To solve we need to isolate the $x$term.
The equation is $2x - (3 - 4x) + 2(x + 5)$.
By removing the bracket and multiplying we get $2x - 3 + 4x + 2x + 10$.
By arranging the similar terms together and adding them we have:
$ \Rightarrow 2x + 4x + 2x - 3 + 10$.
BY further solving we have, $8x + 7$.

Hence the correct answer is $8x + 7$.

Note: Here in this question, we just multiply each term of the first polynomial by each term of the second polynomial and then simplify or if there is any algebraic identity possible we can apply that. This is a question of linear equation in one variable as it can be solved using the basic knowledge of arithmetic operators but while calculating we should be careful as in such types of question calculation mistakes are possible also with the positive and negative signs of the numbers and variables. As we know that if we make the graph of a linear equation it will have a straight line, this will happen when the highest power of the given variable is $1$ .