Solve 1/5left(-1/4x-2right)+7=8/5x

$$\frac{ 1 }{ 5 } \left( - \frac{ 1 }{ 4 } x-2 \right) +7 = \frac{ 8 }{ 5 } x$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{5} by -\frac{1}{4}x-2.

$$\frac{1}{5}\left(-\frac{1}{4}\right)x+\frac{1}{5}\left(-2\right)+7=\frac{8}{5}x$$

Multiply \frac{1}{5} times -\frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\left(-1\right)}{5\times 4}x+\frac{1}{5}\left(-2\right)+7=\frac{8}{5}x$$

Do the multiplications in the fraction \frac{1\left(-1\right)}{5\times 4}.

$$\frac{-1}{20}x+\frac{1}{5}\left(-2\right)+7=\frac{8}{5}x$$

Fraction \frac{-1}{20} can be rewritten as -\frac{1}{20} by extracting the negative sign.

$$-\frac{1}{20}x+\frac{1}{5}\left(-2\right)+7=\frac{8}{5}x$$

Multiply \frac{1}{5} and -2 to get \frac{-2}{5}.

$$-\frac{1}{20}x+\frac{-2}{5}+7=\frac{8}{5}x$$

Fraction \frac{-2}{5} can be rewritten as -\frac{2}{5} by extracting the negative sign.

$$-\frac{1}{20}x-\frac{2}{5}+7=\frac{8}{5}x$$

Convert 7 to fraction \frac{35}{5}.

$$-\frac{1}{20}x-\frac{2}{5}+\frac{35}{5}=\frac{8}{5}x$$

Since -\frac{2}{5} and \frac{35}{5} have the same denominator, add them by adding their numerators.

$$-\frac{1}{20}x+\frac{-2+35}{5}=\frac{8}{5}x$$

Add -2 and 35 to get 33.

$$-\frac{1}{20}x+\frac{33}{5}=\frac{8}{5}x$$

Subtract \frac{8}{5}x from both sides.

$$-\frac{1}{20}x+\frac{33}{5}-\frac{8}{5}x=0$$

Combine -\frac{1}{20}x and -\frac{8}{5}x to get -\frac{33}{20}x.

$$-\frac{33}{20}x+\frac{33}{5}=0$$

Subtract \frac{33}{5} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{33}{20}x=-\frac{33}{5}$$

Multiply both sides by -\frac{20}{33}, the reciprocal of -\frac{33}{20}.

$$x=-\frac{33}{5}\left(-\frac{20}{33}\right)$$

Multiply -\frac{33}{5} times -\frac{20}{33} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-33\left(-20\right)}{5\times 33}$$

Do the multiplications in the fraction \frac{-33\left(-20\right)}{5\times 33}.

$$x=\frac{660}{165}$$

Divide 660 by 165 to get 4.

$$x=4$$