Question

How do you solve $ - 3x + 5 = 2x - 10$

Answer 1

Hint: In this question, we have a single variable linear equation and we are supposed to find the value of the given variable. Use a basic single variable method by shifting variables on one side and constants on the other side, so that it becomes easier to solve the equation. On doing some simplification we get the final answer.

Complete step-by-step solution:
Now, we are given an equation,
$ - 3x + 5 = 2x - 10$
Shifting the variables on one side and the constants on the other side, since we can add constants and same type of variables,
$ \Rightarrow 10 + 5 = 2x + 3x$
Adding the constants and also the variables, since the variables are same
$ \Rightarrow 15 = 5x$
Now, we can see that the variable has a number being multiplied to it, so we will shift it to the LHS, and divide the LHS with it, since the number multiplied to the variable will go to the LHS and perform division.
$ \Rightarrow \dfrac{{15}}{5} = x$
We know that $15$ is divisible by $5$,
Doing basic division,
$ \Rightarrow 3 = x$
Altering the equation,
$ \Rightarrow x = 3$

So, the value has come up as $x = 3$

Note: Variables can only be added if and only if they are the same. Two different variables cannot be added, unless their values are known. Now since this is a single variable equation, all the numbers that have a variable have the same variable. Such types of equations are also called linear equations.
Now we have to check the answer whether it is correct or not
Putting $x = 3$, in the equation to check,
$ \Rightarrow - 3(3) + 5 = 2(3) - 10$
Multiplying the numbers inside the brackets with the numbers that are outside the bracket,
$ \Rightarrow ( - 9) + 5 = 6 - 10$
Taking out the brackets,
$ \Rightarrow - 9 + 5 = 6 - 10$
$ \Rightarrow - 4 = - 4$
Hence, for the equation $ - 3x + 5 = 2x - 10$ the value is $x = 3$