Question

How do you solve the linear equation $-2x-13=-x-27?$

Answer 1

Hint: We will transpose the terms accordingly in the given equation. We will shift the constant term from the left-hand side to the right-hand side of the equation whereas we will shift the variable term from the right-hand side to the left-hand side of the equation.

Complete step-by-step solution:
Let us consider the given equation, $-2x-13=-x-27.$
We are asked to solve the given equation.
We can see that the signs of all the terms in the equation are negative. So, without losing generality, let us multiply the whole equation with $-1$ so that the signs of the terms will become positive.
When we multiply the whole equation with $-1,$ we will get $2x+13=x+27.$
Let us transpose the terms accordingly so that we can find the value of the unknown variable $x.$
First, let us consider the variable terms. Let us take them to the same side. So, we are going to transpose the variable term on the right-hand side.
So, this will give us, $2x-x+13=27.$
As we can see, the positive term became negative after we transposed it.
Now, we are going to transpose the constant term from the left-hand side to the right-hand side. We will yield, $2x-x=27-13.$
Now, we can apply the operations given on the terms separately.
We will get $x=14.$ Here, we applied the subtraction on the coefficients of the variable terms on the left-hand side whereas we applied usual subtraction on the right-hand side.
Hence the solution is $x=14.$

Note: It is not necessary to multiply the equation at the early stage of the procedure. Because, we can still transpose the terms and find the solution as $-2x+x=-27+13\Rightarrow -x=-14\Rightarrow x=14.$ As shown here, we can change the sign in the last step.