Solve 90-19x-19(1/5-3/2x)=0

$$90 - 19 x - 19 ( \frac { 1 } { 5 } - \frac { 3 } { 2 } x ) = 0$$

Solve for x

$$x = -\frac{862}{95} = -9\frac{7}{95} \approx -9.073684211$$

Steps for Solving Linear Equation

Use the distributive property to multiply -19 by \frac{1}{5}-\frac{3}{2}x.

$$90-19x-19\times \frac{1}{5}-19\left(-\frac{3}{2}\right)x=0$$

Multiply -19 and \frac{1}{5} to get \frac{-19}{5}.

$$90-19x+\frac{-19}{5}-19\left(-\frac{3}{2}\right)x=0$$

Fraction \frac{-19}{5} can be rewritten as -\frac{19}{5} by extracting the negative sign.

$$90-19x-\frac{19}{5}-19\left(-\frac{3}{2}\right)x=0$$

Express -19\left(-\frac{3}{2}\right) as a single fraction.

$$90-19x-\frac{19}{5}+\frac{-19\left(-3\right)}{2}x=0$$

Multiply -19 and -3 to get 57.

$$90-19x-\frac{19}{5}+\frac{57}{2}x=0$$

Convert 90 to fraction \frac{450}{5}.

$$\frac{450}{5}-19x-\frac{19}{5}+\frac{57}{2}x=0$$

Since \frac{450}{5} and \frac{19}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{450-19}{5}-19x+\frac{57}{2}x=0$$

Subtract 19 from 450 to get 431.

$$\frac{431}{5}-19x+\frac{57}{2}x=0$$

Combine -19x and \frac{57}{2}x to get \frac{19}{2}x.

$$\frac{431}{5}+\frac{19}{2}x=0$$

Subtract \frac{431}{5} from both sides. Anything subtracted from zero gives its negation.

$$\frac{19}{2}x=-\frac{431}{5}$$

Multiply both sides by \frac{2}{19}, the reciprocal of \frac{19}{2}.

$$x=-\frac{431}{5}\times \frac{2}{19}$$

Multiply -\frac{431}{5} times \frac{2}{19} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-431\times 2}{5\times 19}$$

Do the multiplications in the fraction \frac{-431\times 2}{5\times 19}.

$$x=\frac{-862}{95}$$

Fraction \frac{-862}{95} can be rewritten as -\frac{862}{95} by extracting the negative sign.

$$x=-\frac{862}{95}$$