Solve 1/2x+1/5=-4(3/4x+5)

$$\frac { 1 } { 2 } x + \frac { 1 } { 5 } = - 4 ( \frac { 3 } { 4 } x + 5 )$$

Solve for x

$$x = -\frac{202}{35} = -5\frac{27}{35} \approx -5.771428571$$

Steps for Solving Linear Equation

Use the distributive property to multiply -4 by \frac{3}{4}x+5.

$$\frac{1}{2}x+\frac{1}{5}=-4\times \frac{3}{4}x-20$$

Multiply -4 times \frac{3}{4}.

$$\frac{1}{2}x+\frac{1}{5}=-3x-20$$

Add 3x to both sides.

$$\frac{1}{2}x+\frac{1}{5}+3x=-20$$

Combine \frac{1}{2}x and 3x to get \frac{7}{2}x.

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

Subtract \frac{1}{5} from both sides.

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

Convert -20 to fraction -\frac{100}{5}.

$$\frac{7}{2}x=-\frac{100}{5}-\frac{1}{5}$$

Since -\frac{100}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{2}x=\frac{-100-1}{5}$$

Subtract 1 from -100 to get -101.

$$\frac{7}{2}x=-\frac{101}{5}$$

Multiply both sides by \frac{2}{7}, the reciprocal of \frac{7}{2}.

$$x=-\frac{101}{5}\times \frac{2}{7}$$

Multiply -\frac{101}{5} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-101\times 2}{5\times 7}$$

Do the multiplications in the fraction \frac{-101\times 2}{5\times 7}.

$$x=\frac{-202}{35}$$

Fraction \frac{-202}{35} can be rewritten as -\frac{202}{35} by extracting the negative sign.

$$x=-\frac{202}{35}$$