Solve -6x=1/2*4*49/16-3/2-8

$$- 6 x = \frac { 1 } { 2 } \times 4 \times \frac { 49 } { 16 } - \frac { 3 } { 2 } - 8$$

Solve for x

$$x=\frac{9}{16}=0.5625$$

Steps for Solving Linear Equation

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

$$-6x=\frac{4}{2}\times \frac{49}{16}-\frac{3}{2}-8$$

Divide 4 by 2 to get 2.

$$-6x=2\times \frac{49}{16}-\frac{3}{2}-8$$

Express 2\times \frac{49}{16} as a single fraction.

$$-6x=\frac{2\times 49}{16}-\frac{3}{2}-8$$

Multiply 2 and 49 to get 98.

$$-6x=\frac{98}{16}-\frac{3}{2}-8$$

Reduce the fraction \frac{98}{16} to lowest terms by extracting and canceling out 2.

$$-6x=\frac{49}{8}-\frac{3}{2}-8$$

Least common multiple of 8 and 2 is 8. Convert \frac{49}{8} and \frac{3}{2} to fractions with denominator 8.

$$-6x=\frac{49}{8}-\frac{12}{8}-8$$

Since \frac{49}{8} and \frac{12}{8} have the same denominator, subtract them by subtracting their numerators.

$$-6x=\frac{49-12}{8}-8$$

Subtract 12 from 49 to get 37.

$$-6x=\frac{37}{8}-8$$

Convert 8 to fraction \frac{64}{8}.

$$-6x=\frac{37}{8}-\frac{64}{8}$$

Since \frac{37}{8} and \frac{64}{8} have the same denominator, subtract them by subtracting their numerators.

$$-6x=\frac{37-64}{8}$$

Subtract 64 from 37 to get -27.

$$-6x=-\frac{27}{8}$$

Divide both sides by -6.

$$x=\frac{-\frac{27}{8}}{-6}$$

Express \frac{-\frac{27}{8}}{-6} as a single fraction.

$$x=\frac{-27}{8\left(-6\right)}$$

Multiply 8 and -6 to get -48.

$$x=\frac{-27}{-48}$$

Reduce the fraction \frac{-27}{-48} to lowest terms by extracting and canceling out -3.

$$x=\frac{9}{16}$$