17. $\frac{1}{2} r+2\left(\frac{3}{4} r-1\right)=\frac{1}{4} r+6$

Step 1 ：The given equation is \(\frac{1}{2} r+2\left(\frac{3}{4} r-1\right)=\frac{1}{4} r+6\).

Step 2 ：This is a linear equation in terms of 'r'. To solve for 'r', we need to simplify the equation and isolate 'r' on one side of the equation.

Step 3 ：First, distribute the 2 in the term \(2\left(\frac{3}{4} r-1\right)\) to get \(\frac{3}{2} r - 2\).

Step 4 ：Substitute this back into the equation to get \(\frac{1}{2} r + \frac{3}{2} r - 2 = \frac{1}{4} r + 6\).

Step 5 ：Combine like terms to get \(2r - 2 = \frac{1}{4} r + 6\).

Step 6 ：Subtract \(\frac{1}{4} r\) from both sides to get \(1.75r - 2 = 6\).

Step 7 ：Add 2 to both sides to get \(1.75r = 8\).

Step 8 ：Finally, divide both sides by 1.75 to solve for 'r'.

Step 9 ：The solution to the equation is approximately 4.57. This is the value of 'r' that satisfies the equation.

Step 10 ：Final Answer: The solution to the equation is \(\boxed{4.57}\).