Solve 6/5x+7/16=x-3/2

$$\frac { 6 } { 5 } x + \frac { 7 } { 16 } = x - \frac { 3 } { 2 }$$

Solve for x

$$x = -\frac{155}{16} = -9\frac{11}{16} = -9.6875$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$\frac{6}{5}x+\frac{7}{16}-x=-\frac{3}{2}$$

Combine \frac{6}{5}x and -x to get \frac{1}{5}x.

$$\frac{1}{5}x+\frac{7}{16}=-\frac{3}{2}$$

Subtract \frac{7}{16} from both sides.

$$\frac{1}{5}x=-\frac{3}{2}-\frac{7}{16}$$

Least common multiple of 2 and 16 is 16. Convert -\frac{3}{2} and \frac{7}{16} to fractions with denominator 16.

$$\frac{1}{5}x=-\frac{24}{16}-\frac{7}{16}$$

Since -\frac{24}{16} and \frac{7}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{5}x=\frac{-24-7}{16}$$

Subtract 7 from -24 to get -31.

$$\frac{1}{5}x=-\frac{31}{16}$$

Multiply both sides by 5, the reciprocal of \frac{1}{5}.

$$x=-\frac{31}{16}\times 5$$

Express -\frac{31}{16}\times 5 as a single fraction.

$$x=\frac{-31\times 5}{16}$$

Multiply -31 and 5 to get -155.

$$x=\frac{-155}{16}$$

Fraction \frac{-155}{16} can be rewritten as -\frac{155}{16} by extracting the negative sign.

$$x=-\frac{155}{16}$$