Solve 1/4=5/9x+5/2

$$\frac { 1 } { 4 } = \frac { 5 } { 9 } x + \frac { 5 } { 2 }$$

Solve for x

$$x = -\frac{81}{20} = -4\frac{1}{20} = -4.05$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$\frac{5}{9}x+\frac{5}{2}=\frac{1}{4}$$

Subtract \frac{5}{2} from both sides.

$$\frac{5}{9}x=\frac{1}{4}-\frac{5}{2}$$

Least common multiple of 4 and 2 is 4. Convert \frac{1}{4} and \frac{5}{2} to fractions with denominator 4.

$$\frac{5}{9}x=\frac{1}{4}-\frac{10}{4}$$

Since \frac{1}{4} and \frac{10}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{9}x=\frac{1-10}{4}$$

Subtract 10 from 1 to get -9.

$$\frac{5}{9}x=-\frac{9}{4}$$

Multiply both sides by \frac{9}{5}, the reciprocal of \frac{5}{9}.

$$x=-\frac{9}{4}\times \frac{9}{5}$$

Multiply -\frac{9}{4} times \frac{9}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-9\times 9}{4\times 5}$$

Do the multiplications in the fraction \frac{-9\times 9}{4\times 5}.

$$x=\frac{-81}{20}$$

Fraction \frac{-81}{20} can be rewritten as -\frac{81}{20} by extracting the negative sign.

$$x=-\frac{81}{20}$$