Question

question
solve for ( x ):
( -6x = -(x - 9) + 1 )

Explanation:

Step1: Simplify the right - hand side

First, we need to simplify the right - hand side of the equation \(-6x=-(x - 9)+1\). Using the distributive property \(a(b + c)=ab+ac\) (here \(a=- 1\), \(b = x\), \(c=-9\)), we get \(-(x - 9)=-x + 9\). So the equation becomes \(-6x=-x + 9+1\). Then, combine like terms on the right - hand side: \(9 + 1=10\), so the equation is \(-6x=-x + 10\).

Step2: Isolate the variable \(x\)

Add \(x\) to both sides of the equation \(-6x=-x + 10\) to get all the \(x\) terms on one side. \(-6x+x=-x + 10+x\). Combining like terms, \(-6x+x=-5x\) and \(-x + x = 0\), so we have \(-5x=10\).

Step3: Solve for \(x\)

Divide both sides of the equation \(-5x = 10\) by \(-5\). \(\frac{-5x}{-5}=\frac{10}{-5}\). Simplifying both sides, we get \(x=-2\).

Answer:

\(x = - 2\)