Question

Solve the equation if possible. $$ 4 n=-28 n-3 $$

Short answer

The solution to the equation \(4n = -28n - 3\) is \(n = -3/32\).

Step-by-step solution

Simplify the equation

In the equation \(4n = -28n - 3\), begin by moving terms involving 'n' to one side and constants to the other side to simplify the equation. Achieve this by adding \(28n\) to both sides to get \(4n + 28n = -3\). This can be simplified further into \(32n = -3\).

Solve for 'n'

Now, to find the value of the variable 'n', divide both sides of the equation by '32' to get \(n = -3/32\)

Verify the solution

The solution to the equation can be verified by substituting the calculated value of 'n' into the original equation to see if both sides are equal. The original equation is \(4n = -28n - 3\), substituting \( n = -3/32 \) we get \(4(-3/32) = -28(-3/32) - 3\), which simplifies to \(-3/8 = 21/8 - 3\), that further simplifies to \(-3/8 = -3/8\). Since both sides are equal, it verifies that our solution is correct.