Solve -9x+55=1/2(-2x+17+x)

$$-9x+55= \frac{ 1 }{ 2 } (-2x+17+x)$$

Solve for x

$$x = \frac{93}{17} = 5\frac{8}{17} \approx 5.470588235$$

Steps for Solving Linear Equation

Combine -2x and x to get -x.

$$-9x+55=\frac{1}{2}\left(-x+17\right)$$

Use the distributive property to multiply \frac{1}{2} by -x+17.

$$-9x+55=\frac{1}{2}\left(-1\right)x+\frac{1}{2}\times 17$$

Multiply \frac{1}{2} and -1 to get -\frac{1}{2}.

$$-9x+55=-\frac{1}{2}x+\frac{1}{2}\times 17$$

Multiply \frac{1}{2} and 17 to get \frac{17}{2}.

$$-9x+55=-\frac{1}{2}x+\frac{17}{2}$$

Add \frac{1}{2}x to both sides.

$$-9x+55+\frac{1}{2}x=\frac{17}{2}$$

Combine -9x and \frac{1}{2}x to get -\frac{17}{2}x.

$$-\frac{17}{2}x+55=\frac{17}{2}$$

Subtract 55 from both sides.

$$-\frac{17}{2}x=\frac{17}{2}-55$$

Convert 55 to fraction \frac{110}{2}.

$$-\frac{17}{2}x=\frac{17}{2}-\frac{110}{2}$$

Since \frac{17}{2} and \frac{110}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{17}{2}x=\frac{17-110}{2}$$

Subtract 110 from 17 to get -93.

$$-\frac{17}{2}x=-\frac{93}{2}$$

Multiply both sides by -\frac{2}{17}, the reciprocal of -\frac{17}{2}.

$$x=-\frac{93}{2}\left(-\frac{2}{17}\right)$$

Multiply -\frac{93}{2} times -\frac{2}{17} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-93\left(-2\right)}{2\times 17}$$

Do the multiplications in the fraction \frac{-93\left(-2\right)}{2\times 17}.

$$x=\frac{186}{34}$$

Reduce the fraction \frac{186}{34} to lowest terms by extracting and canceling out 2.

$$x=\frac{93}{17}$$