Question

1. solve for ( x ):( x + 9 = 6x - 31 ) (with some handwritten steps below the equation)

Explanation:

Step1: Subtract \(x\) from both sides

To isolate the variable terms, we subtract \(x\) from each side of the equation \(x + 9=6x - 31\). This gives us \(9 = 5x - 31\) (because \(x - x = 0\) on the left and \(6x - x = 5x\) on the right).

Step2: Add 31 to both sides

Next, we add 31 to both sides to isolate the term with \(x\). So, \(9+31 = 5x - 31 + 31\), which simplifies to \(40 = 5x\) (since \(-31 + 31 = 0\) on the right).

Step3: Divide by 5

Finally, we divide both sides by 5 to solve for \(x\). \(\frac{40}{5}=\frac{5x}{5}\), which gives \(x = 8\).

Answer:

\(x = 8\)