Solve a/2+2/3=3a/5+5/7

$$\frac { a } { 2 } + \frac { 2 } { 3 } = \frac { 3 a } { 5 } + \frac { 5 } { 7 }$$

Solve for a

$$a=-\frac{10}{21}\approx -0.476190476$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 210, the least common multiple of 2,3,5,7.

$$105a+140=42\times 3a+150$$

Multiply 42 and 3 to get 126.

$$105a+140=126a+150$$

Subtract 126a from both sides.

$$105a+140-126a=150$$

Combine 105a and -126a to get -21a.

$$-21a+140=150$$

Subtract 140 from both sides.

$$-21a=150-140$$

Subtract 140 from 150 to get 10.

$$-21a=10$$

Divide both sides by -21.

$$a=\frac{10}{-21}$$

Fraction \frac{10}{-21} can be rewritten as -\frac{10}{21} by extracting the negative sign.

$$a=-\frac{10}{21}$$