Solve 5/9x+2/15=4/15x-5/18

$$\frac{ 5 }{ 9 } x+ \frac{ 2 }{ 15 } = \frac{ 4 }{ 15 } x- \frac{ 5 }{ 18 }$$

Solve for x

$$x = -\frac{37}{26} = -1\frac{11}{26} \approx -1.423076923$$

Steps for Solving Linear Equation

Subtract \frac{4}{15}x from both sides.

$$\frac{5}{9}x+\frac{2}{15}-\frac{4}{15}x=-\frac{5}{18}$$

Combine \frac{5}{9}x and -\frac{4}{15}x to get \frac{13}{45}x.

$$\frac{13}{45}x+\frac{2}{15}=-\frac{5}{18}$$

Subtract \frac{2}{15} from both sides.

$$\frac{13}{45}x=-\frac{5}{18}-\frac{2}{15}$$

Least common multiple of 18 and 15 is 90. Convert -\frac{5}{18} and \frac{2}{15} to fractions with denominator 90.

$$\frac{13}{45}x=-\frac{25}{90}-\frac{12}{90}$$

Since -\frac{25}{90} and \frac{12}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13}{45}x=\frac{-25-12}{90}$$

Subtract 12 from -25 to get -37.

$$\frac{13}{45}x=-\frac{37}{90}$$

Multiply both sides by \frac{45}{13}, the reciprocal of \frac{13}{45}.

$$x=-\frac{37}{90}\times \frac{45}{13}$$

Multiply -\frac{37}{90} times \frac{45}{13} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-37\times 45}{90\times 13}$$

Do the multiplications in the fraction \frac{-37\times 45}{90\times 13}.

$$x=\frac{-1665}{1170}$$

Reduce the fraction \frac{-1665}{1170} to lowest terms by extracting and canceling out 45.

$$x=-\frac{37}{26}$$