Question

How do you solve $ - 4x - 1 = - 7 $ ?

Answer 1

Hint: To solve this linear equation in one variable, the only thing you will have to do is solve for x. And to do that, you will have to bring -1 to the RHS first. This will make the RHS equal to -6. Now divide the whole equation by 2 which will give you $ - 2x = - 3 $ . Now, again divide the whole equation by 2, which will give you $ - x = - \dfrac{3}{2} $ . Now multiply RHS and LHS by-1 to remove the negative sign.

Complete step-by-step solution:
The given question we have is $ - 4x - 1 = - 7 $
Now, to solve this type of problem, all we have to do is to bring the unknown variables on the same side of the equation and then get the value from the other side. This process is the same to solve any linear equation with a single variable.
Therefore, bringing the like terms on the same side of the equation and solving we get;-
 $
   - 4x = - 7 + 1 \\
   = - 6 \\
 $
Now, dividing both the sides by 2, we will get
 $
   - 4x = - 6 \\
   \Rightarrow \dfrac{{ - 4x}}{2} = \dfrac{{ - 6}}{2} \\
   \Rightarrow - 2x = - 3 \\
 $
Again, dividing the whole equation by 2, we will get:-
 $
   - 2x = - 3 \\
   \Rightarrow \dfrac{{ - 2x}}{2} = \dfrac{{ - 3}}{2} \\
   \Rightarrow - x = \dfrac{{ - 3}}{2} \\
 $
To remove the negative sign, multiplying both the sides by -1, we will get:-
 $
   - x = \dfrac{{ - 3}}{2} \\
   \Rightarrow - x \times - 1 = \dfrac{{ - 3}}{2} \times - 1 \\
   \Rightarrow x = \dfrac{3}{2} \\
 $
Hence, we can conclude that $ - x = - \dfrac{3}{2} $ is the answer

Note: Solution of linear equation with single variable is quite easy to find. The only thing that people do wrong while solving a linear equation with a single variable is that they do the basic mathematical operations wrong. So take care of all the operations you do while solving and look how you ace this chapter.