Solve 2/3w+4=-1/4w-5/4

$$\frac { 2 } { 3 } w + 4 = - \frac { 1 } { 4 } w - \frac { 5 } { 4 }$$

Solve for w

$$w = -\frac{63}{11} = -5\frac{8}{11} \approx -5.727272727$$

Steps for Solving Linear Equation

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

$$\frac{2}{3}w+4+\frac{1}{4}w=-\frac{5}{4}$$

Combine \frac{2}{3}w and \frac{1}{4}w to get \frac{11}{12}w.

$$\frac{11}{12}w+4=-\frac{5}{4}$$

Subtract 4 from both sides.

$$\frac{11}{12}w=-\frac{5}{4}-4$$

Convert 4 to fraction \frac{16}{4}.

$$\frac{11}{12}w=-\frac{5}{4}-\frac{16}{4}$$

Since -\frac{5}{4} and \frac{16}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{12}w=\frac{-5-16}{4}$$

Subtract 16 from -5 to get -21.

$$\frac{11}{12}w=-\frac{21}{4}$$

Multiply both sides by \frac{12}{11}, the reciprocal of \frac{11}{12}.

$$w=-\frac{21}{4}\times \frac{12}{11}$$

Multiply -\frac{21}{4} times \frac{12}{11} by multiplying numerator times numerator and denominator times denominator.

$$w=\frac{-21\times 12}{4\times 11}$$

Do the multiplications in the fraction \frac{-21\times 12}{4\times 11}.

$$w=\frac{-252}{44}$$

Reduce the fraction \frac{-252}{44} to lowest terms by extracting and canceling out 4.

$$w=-\frac{63}{11}$$