Question

-x + 6 = -2(x + 2) - 5

Explanation:

Step1: Expand the right - hand side

First, we need to expand the right - hand side of the equation \(-x + 6=-2(x + 2)-5\). Using the distributive property \(a(b + c)=ab+ac\), where \(a=-2\), \(b = x\) and \(c = 2\), we get \(-2(x + 2)=-2x-4\). So the equation becomes \(-x + 6=-2x-4 - 5\).

Step2: Simplify the right - hand side

Simplify the constants on the right - hand side: \(-4-5=-9\). So the equation is now \(-x + 6=-2x-9\).

Step3: Add \(2x\) to both sides

To get all the \(x\) terms on one side, we add \(2x\) to both sides of the equation. \(-x+2x + 6=-2x + 2x-9\), which simplifies to \(x + 6=-9\).

Step4: Subtract 6 from both sides

Subtract 6 from both sides to solve for \(x\): \(x+6 - 6=-9 - 6\).

Answer:

\(x=-15\)