Solve 4(-46)/x+20=-47/frac{7{2}}-3

$$\frac { 4 ( - 46 ) } { x } + 20 = \frac { - 47 } { \frac { 7 } { 2 } } - 3$$

Solve for x

$$x = \frac{1288}{255} = 5\frac{13}{255} \approx 5.050980392$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$4\left(-46\right)+x\times 20=x\times \frac{-47}{\frac{7}{2}}+x\left(-3\right)$$

Multiply 4 and -46 to get -184.

$$-184+x\times 20=x\times \frac{-47}{\frac{7}{2}}+x\left(-3\right)$$

Divide -47 by \frac{7}{2} by multiplying -47 by the reciprocal of \frac{7}{2}.

$$-184+x\times 20=x\left(-47\right)\times \frac{2}{7}+x\left(-3\right)$$

Express -47\times \frac{2}{7} as a single fraction.

$$-184+x\times 20=x\times \frac{-47\times 2}{7}+x\left(-3\right)$$

Multiply -47 and 2 to get -94.

$$-184+x\times 20=x\times \frac{-94}{7}+x\left(-3\right)$$

Fraction \frac{-94}{7} can be rewritten as -\frac{94}{7} by extracting the negative sign.

$$-184+x\times 20=x\left(-\frac{94}{7}\right)+x\left(-3\right)$$

Combine x\left(-\frac{94}{7}\right) and x\left(-3\right) to get -\frac{115}{7}x.

$$-184+x\times 20=-\frac{115}{7}x$$

Add \frac{115}{7}x to both sides.

$$-184+x\times 20+\frac{115}{7}x=0$$

Combine x\times 20 and \frac{115}{7}x to get \frac{255}{7}x.

$$-184+\frac{255}{7}x=0$$

Add 184 to both sides. Anything plus zero gives itself.

$$\frac{255}{7}x=184$$

Multiply both sides by \frac{7}{255}, the reciprocal of \frac{255}{7}.

$$x=184\times \frac{7}{255}$$

Express 184\times \frac{7}{255} as a single fraction.

$$x=\frac{184\times 7}{255}$$

Multiply 184 and 7 to get 1288.

$$x=\frac{1288}{255}$$