Solve S_{5}=2(1/32-11/frac{1{2}-1}=

$$S _ { 5 } = \frac { 2 ( \frac { 1 } { 32 } - 11 } { \frac { 1 } { 2 } - 1 } =$$

Solve for S_5

$$S_{5} = \frac{351}{8} = 43\frac{7}{8} = 43.875$$

Steps for Solving Linear Equation

Convert 11 to fraction \frac{352}{32}.

$$S_{5}=\frac{2\left(\frac{1}{32}-\frac{352}{32}\right)}{\frac{1}{2}-1}$$

Since \frac{1}{32} and \frac{352}{32} have the same denominator, subtract them by subtracting their numerators.

$$S_{5}=\frac{2\times \frac{1-352}{32}}{\frac{1}{2}-1}$$

Subtract 352 from 1 to get -351.

$$S_{5}=\frac{2\left(-\frac{351}{32}\right)}{\frac{1}{2}-1}$$

Express 2\left(-\frac{351}{32}\right) as a single fraction.

$$S_{5}=\frac{\frac{2\left(-351\right)}{32}}{\frac{1}{2}-1}$$

Multiply 2 and -351 to get -702.

$$S_{5}=\frac{\frac{-702}{32}}{\frac{1}{2}-1}$$

Reduce the fraction \frac{-702}{32} to lowest terms by extracting and canceling out 2.

$$S_{5}=\frac{-\frac{351}{16}}{\frac{1}{2}-1}$$

Convert 1 to fraction \frac{2}{2}.

$$S_{5}=\frac{-\frac{351}{16}}{\frac{1}{2}-\frac{2}{2}}$$

Since \frac{1}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

$$S_{5}=\frac{-\frac{351}{16}}{\frac{1-2}{2}}$$

Subtract 2 from 1 to get -1.

$$S_{5}=\frac{-\frac{351}{16}}{-\frac{1}{2}}$$

Divide -\frac{351}{16} by -\frac{1}{2} by multiplying -\frac{351}{16} by the reciprocal of -\frac{1}{2}.

$$S_{5}=-\frac{351}{16}\left(-2\right)$$

Express -\frac{351}{16}\left(-2\right) as a single fraction.

$$S_{5}=\frac{-351\left(-2\right)}{16}$$

Multiply -351 and -2 to get 702.

$$S_{5}=\frac{702}{16}$$

Reduce the fraction \frac{702}{16} to lowest terms by extracting and canceling out 2.

$$S_{5}=\frac{351}{8}$$

Assign S_5

$$S_{5}≔\frac{351}{8}$$