Question

23 - 8(2 + 7n) = -6n + 34

Explanation:

Step1: Expand the left - hand side

Using the distributive property \(a(b + c)=ab+ac\), for \(- 8(2 + 7n)\), we have \(-8\times2-8\times7n=-16 - 56n\). So the original equation \(23-8(2 + 7n)=-6n + 34\) becomes \(23-16-56n=-6n + 34\).

Step2: Simplify the left - hand side

Calculate \(23-16 = 7\), so the equation is \(7-56n=-6n + 34\).

Step3: Move the terms with \(n\) to one side

Add \(56n\) to both sides of the equation: \(7-56n + 56n=-6n+56n + 34\), which simplifies to \(7 = 50n+34\).

Step4: Isolate the term with \(n\)

Subtract 34 from both sides: \(7-34=50n+34 - 34\), so \(-27 = 50n\).

Step5: Solve for \(n\)

Divide both sides by 50: \(n=\frac{-27}{50}=-0.54\)

Answer:

\(n =-\frac{27}{50}\) (or \(n=-0.54\))