6. What is the solution to the equation 7w-2(w-9)=4-8(w+2) ?

To solve the equation \(7w - 2(w - 9) = 4 - 8(w + 2)\), follow these steps:<br /><br />1. Distribute the terms inside the parentheses:<br /> \[<br /> 7w - 2w + 18 = 4 - 8w - 16<br /> \]<br /><br />2. Combine like terms on both sides:<br /> \[<br /> 7w - 2w + 18 = 4 - 16 - 8w<br /> \]<br /> \[<br /> 5w + 18 = -12 - 8w<br /> \]<br /><br />3. Move all terms involving \(w\) to one side and constant terms to the other side:<br /> \[<br /> 5w + 8w = -12 - 18<br /> \]<br /> \[<br /> 13w = -30<br /> \]<br /><br />4. Solve for \(w\):<br /> \[<br /> w = \frac{-30}{13}<br /> \]<br /><br />So, the solution to the equation is:<br />\[<br />w = -\frac{30}{13}<br />\]