Solve 1/2(x-3/4)-8x=40x

$$\frac { 1 } { 2 } ( x - \frac { 3 } { 4 } ) - 8 x = 40 x$$

Solve for x

$$x=-\frac{3}{380}\approx -0.007894737$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by x-\frac{3}{4}.

$$\frac{1}{2}x+\frac{1}{2}\left(-\frac{3}{4}\right)-8x=40x$$

Multiply \frac{1}{2} times -\frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}x+\frac{1\left(-3\right)}{2\times 4}-8x=40x$$

Do the multiplications in the fraction \frac{1\left(-3\right)}{2\times 4}.

$$\frac{1}{2}x+\frac{-3}{8}-8x=40x$$

Fraction \frac{-3}{8} can be rewritten as -\frac{3}{8} by extracting the negative sign.

$$\frac{1}{2}x-\frac{3}{8}-8x=40x$$

Combine \frac{1}{2}x and -8x to get -\frac{15}{2}x.

$$-\frac{15}{2}x-\frac{3}{8}=40x$$

Subtract 40x from both sides.

$$-\frac{15}{2}x-\frac{3}{8}-40x=0$$

Combine -\frac{15}{2}x and -40x to get -\frac{95}{2}x.

$$-\frac{95}{2}x-\frac{3}{8}=0$$

Add \frac{3}{8} to both sides. Anything plus zero gives itself.

$$-\frac{95}{2}x=\frac{3}{8}$$

Multiply both sides by -\frac{2}{95}, the reciprocal of -\frac{95}{2}.

$$x=\frac{3}{8}\left(-\frac{2}{95}\right)$$

Multiply \frac{3}{8} times -\frac{2}{95} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{3\left(-2\right)}{8\times 95}$$

Do the multiplications in the fraction \frac{3\left(-2\right)}{8\times 95}.

$$x=\frac{-6}{760}$$

Reduce the fraction \frac{-6}{760} to lowest terms by extracting and canceling out 2.

$$x=-\frac{3}{380}$$