Question

solve the linear equation for n.
if no solution exists, enter no solution. if the equation has infinite solutions, enter all real numbers.
10 - 5n = -3 + 4n + 4
show your work here

Explanation:

Step1: Simplify the right side

First, we simplify the right - hand side of the equation \(10 - 5n=-3 + 4n+4\). Combine the constant terms \(-3\) and \(4\): \(-3 + 4=1\). So the equation becomes \(10-5n = 4n + 1\).

Step2: Move all n terms to one side

Next, we want to get all the terms with \(n\) on one side. Add \(5n\) to both sides of the equation: \(10-5n + 5n=4n+1 + 5n\). This simplifies to \(10=9n + 1\).

Step3: Move the constant term to the other side

Then, subtract \(1\) from both sides: \(10 - 1=9n+1 - 1\). Which gives us \(9 = 9n\).

Step4: Solve for n

Finally, divide both sides by \(9\): \(\frac{9}{9}=\frac{9n}{9}\), so \(n = 1\).

Answer:

\(n = 1\)