Question

For what value of n is $\frac{-4+\left(-3\right)+5+4+\left(-3\right)+n}{-7}=0$true?

Short answer

The value of n is 1

Step-by-step solution

What is the equation of integers? 

In the equation with integers, when you add or subtract the same quantity from both sides of an equation, you still have equality. For any numbers a, b, c, if a = b then a + c = b + c or if a = b then a − c = b − c .

How to solve an equation with integers?

Solve Equations with Integers Using the Addition and Subtraction Properties of Equality

In Solve Equations with the Subtraction and Addition Properties of Equality, we solved equations similar to the two shown here using the Subtraction and Addition Properties of Equality. Now we can use them again with integers.

$\begin{array}{l}x+4=12y-5=15\\ x+4-4=12-4y-5+5=15+5\\ x=8y=20\end{array}$

For what value of n is -4+-3+5+4+-3+n-7=0 true?

The equation provided in the question,

$\frac{-4+\left(-3\right)+5+4+\left(-3\right)+n}{-7}=0$

1. Multiply both sides of the equation with$-7$and solve:

$- 1 + n = 0$

$- 1 + 1 + n = 0 + 1 [ \text{add} \text{1} \text{to} \text{both} \text{sides} ]$$[\Rightarrow n = 1]$

The value of $n$ is 1