Question

The sum of two integers is 48. If one of the integers is -24. Determine the other.

Answer 1

Hint: First, we will consider that let the required integer be $x$. Use the given information to form an equation in $x$. Take -24 to the other side and then solve the equation and find the value of $x$. If a term of subtraction is taken to the other side, the sign gets reversed.

Complete step-by-step answer:

Let the integer be $x$.
We are given that the sum of integers is 48 and one of them is -24.
That is, If we add $x$ and -24, we will get 48.
We can rewrite the given statement as,
$x + \left( { - 24} \right) = 48$
Now, we will solve the brackets. As, we know, \[ - \left( { + a} \right) = - a\], therefore, $x + \left( { - 24} \right) = 48$ can be written as, $x - 24 = 48$
We can solve the equation by taking -24 to the other side. When we bring one number from one side to the other side, the sign is reversed.
Thus, 24 will be added to 48 on the right- hand- side.
$\Rightarrow$$x = 48 + 24$
Add 48 and 24 to find the value of $x$.
$\Rightarrow$$x = 92$
Thus, the other integer is 92.

Note: Integers can be positive, negative or zero. Also, \[ - \left( { + a} \right) = - a\], \[ - \left( { - a} \right) = a\], \[ - \left( { + a} \right) = - a\] and \[ + \left( { + a} \right) = a\]. When we bring one number from one side to the other side, the sign is reversed, addition is changed to subtraction and vice-versa; multiplication is changed to division and vice-versa.