Solve 1/4x+8/9=-6/12

$$\frac{ 1 }{ 4 } x+ \frac{ 8 }{ 9 } = \frac{ -6 }{ 12 }$$

Solve for x

$$x = -\frac{50}{9} = -5\frac{5}{9} \approx -5.555555556$$

Steps for Solving Linear Equation

Reduce the fraction \frac{-6}{12} to lowest terms by extracting and canceling out 6.

$$\frac{1}{4}x+\frac{8}{9}=-\frac{1}{2}$$

Subtract \frac{8}{9} from both sides.

$$\frac{1}{4}x=-\frac{1}{2}-\frac{8}{9}$$

Least common multiple of 2 and 9 is 18. Convert -\frac{1}{2} and \frac{8}{9} to fractions with denominator 18.

$$\frac{1}{4}x=-\frac{9}{18}-\frac{16}{18}$$

Since -\frac{9}{18} and \frac{16}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4}x=\frac{-9-16}{18}$$

Subtract 16 from -9 to get -25.

$$\frac{1}{4}x=-\frac{25}{18}$$

Multiply both sides by 4, the reciprocal of \frac{1}{4}.

$$x=-\frac{25}{18}\times 4$$

Express -\frac{25}{18}\times 4 as a single fraction.

$$x=\frac{-25\times 4}{18}$$

Multiply -25 and 4 to get -100.

$$x=\frac{-100}{18}$$

Reduce the fraction \frac{-100}{18} to lowest terms by extracting and canceling out 2.

$$x=-\frac{50}{9}$$