Solve 3/4x-8/5+2/3x-3/1=frac{8}{3}x-frac{186}{3}

$$\frac { 3 } { 4 } x - \frac { 8 } { 5 } + \frac { 2 } { 3 } x - \frac { 3 } { 1 } = \frac { 8 } { 3 } x - \frac { 186 } { 3 }$$

Solve for x

$$x = \frac{1148}{25} = 45\frac{23}{25} = 45.92$$

Steps for Solving Linear Equation

Combine \frac{3}{4}x and \frac{2}{3}x to get \frac{17}{12}x.

$$\frac{17}{12}x-\frac{8}{5}-\frac{3}{1}=\frac{8}{3}x-\frac{186}{3}$$

Anything divided by one gives itself.

$$\frac{17}{12}x-\frac{8}{5}-3=\frac{8}{3}x-\frac{186}{3}$$

Convert 3 to fraction \frac{15}{5}.

$$\frac{17}{12}x-\frac{8}{5}-\frac{15}{5}=\frac{8}{3}x-\frac{186}{3}$$

Since -\frac{8}{5} and \frac{15}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17}{12}x+\frac{-8-15}{5}=\frac{8}{3}x-\frac{186}{3}$$

Subtract 15 from -8 to get -23.

$$\frac{17}{12}x-\frac{23}{5}=\frac{8}{3}x-\frac{186}{3}$$

Divide 186 by 3 to get 62.

$$\frac{17}{12}x-\frac{23}{5}=\frac{8}{3}x-62$$

Subtract \frac{8}{3}x from both sides.

$$\frac{17}{12}x-\frac{23}{5}-\frac{8}{3}x=-62$$

Combine \frac{17}{12}x and -\frac{8}{3}x to get -\frac{5}{4}x.

$$-\frac{5}{4}x-\frac{23}{5}=-62$$

Add \frac{23}{5} to both sides.

$$-\frac{5}{4}x=-62+\frac{23}{5}$$

Convert -62 to fraction -\frac{310}{5}.

$$-\frac{5}{4}x=-\frac{310}{5}+\frac{23}{5}$$

Since -\frac{310}{5} and \frac{23}{5} have the same denominator, add them by adding their numerators.

$$-\frac{5}{4}x=\frac{-310+23}{5}$$

Add -310 and 23 to get -287.

$$-\frac{5}{4}x=-\frac{287}{5}$$

Multiply both sides by -\frac{4}{5}, the reciprocal of -\frac{5}{4}.

$$x=-\frac{287}{5}\left(-\frac{4}{5}\right)$$

Multiply -\frac{287}{5} times -\frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-287\left(-4\right)}{5\times 5}$$

Do the multiplications in the fraction \frac{-287\left(-4\right)}{5\times 5}.

$$x=\frac{1148}{25}$$