Solve 5/3x-3=-1/4x-5/4

$$\frac { 5 } { 3 } x - 3 = - \frac { 1 } { 4 } x - \frac { 5 } { 4 }$$

Solve for x

$$x=\frac{21}{23}\approx 0.913043478$$

Steps for Solving Linear Equation

Add \frac{1}{4}x to both sides.

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

Combine \frac{5}{3}x and \frac{1}{4}x to get \frac{23}{12}x.

$$\frac{23}{12}x-3=-\frac{5}{4}$$

Add 3 to both sides.

$$\frac{23}{12}x=-\frac{5}{4}+3$$

Convert 3 to fraction \frac{12}{4}.

$$\frac{23}{12}x=-\frac{5}{4}+\frac{12}{4}$$

Since -\frac{5}{4} and \frac{12}{4} have the same denominator, add them by adding their numerators.

$$\frac{23}{12}x=\frac{-5+12}{4}$$

Add -5 and 12 to get 7.

$$\frac{23}{12}x=\frac{7}{4}$$

Multiply both sides by \frac{12}{23}, the reciprocal of \frac{23}{12}.

$$x=\frac{7}{4}\times \frac{12}{23}$$

Multiply \frac{7}{4} times \frac{12}{23} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{7\times 12}{4\times 23}$$

Do the multiplications in the fraction \frac{7\times 12}{4\times 23}.

$$x=\frac{84}{92}$$

Reduce the fraction \frac{84}{92} to lowest terms by extracting and canceling out 4.

$$x=\frac{21}{23}$$