Solve 4a-1/9+4-2/1=2a-1/9+2

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

Solve for a

$$a = \frac{142}{9} = 15\frac{7}{9} \approx 15.777777778$$

Steps for Solving Linear Equation

Add 9 and 4 to get 13.

$$\frac{4a-1}{13}-\frac{2}{1}=\frac{2a-1}{9+2}$$

Anything divided by one gives itself.

$$\frac{4a-1}{13}-2=\frac{2a-1}{9+2}$$

Add 9 and 2 to get 11.

$$\frac{4a-1}{13}-2=\frac{2a-1}{11}$$

Divide each term of 4a-1 by 13 to get \frac{4}{13}a-\frac{1}{13}.

$$\frac{4}{13}a-\frac{1}{13}-2=\frac{2a-1}{11}$$

Convert 2 to fraction \frac{26}{13}.

$$\frac{4}{13}a-\frac{1}{13}-\frac{26}{13}=\frac{2a-1}{11}$$

Since -\frac{1}{13} and \frac{26}{13} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{13}a+\frac{-1-26}{13}=\frac{2a-1}{11}$$

Subtract 26 from -1 to get -27.

$$\frac{4}{13}a-\frac{27}{13}=\frac{2a-1}{11}$$

Divide each term of 2a-1 by 11 to get \frac{2}{11}a-\frac{1}{11}.

$$\frac{4}{13}a-\frac{27}{13}=\frac{2}{11}a-\frac{1}{11}$$

Subtract \frac{2}{11}a from both sides.

$$\frac{4}{13}a-\frac{27}{13}-\frac{2}{11}a=-\frac{1}{11}$$

Combine \frac{4}{13}a and -\frac{2}{11}a to get \frac{18}{143}a.

$$\frac{18}{143}a-\frac{27}{13}=-\frac{1}{11}$$

Add \frac{27}{13} to both sides.

$$\frac{18}{143}a=-\frac{1}{11}+\frac{27}{13}$$

Least common multiple of 11 and 13 is 143. Convert -\frac{1}{11} and \frac{27}{13} to fractions with denominator 143.

$$\frac{18}{143}a=-\frac{13}{143}+\frac{297}{143}$$

Since -\frac{13}{143} and \frac{297}{143} have the same denominator, add them by adding their numerators.

$$\frac{18}{143}a=\frac{-13+297}{143}$$

Add -13 and 297 to get 284.

$$\frac{18}{143}a=\frac{284}{143}$$

Multiply both sides by \frac{143}{18}, the reciprocal of \frac{18}{143}.

$$a=\frac{284}{143}\times \frac{143}{18}$$

Multiply \frac{284}{143} times \frac{143}{18} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{284\times 143}{143\times 18}$$

Cancel out 143 in both numerator and denominator.

$$a=\frac{284}{18}$$

Reduce the fraction \frac{284}{18} to lowest terms by extracting and canceling out 2.

$$a=\frac{142}{9}$$