Solve a+7/8a-5=2/3

$$\frac { a + 7 } { 8 a - 5 } = \frac { 2 } { 3 }$$

Solve for a

$$a = \frac{31}{13} = 2\frac{5}{13} \approx 2.384615385$$

Steps for Solving Linear Equation

Variable a cannot be equal to \frac{5}{8} since division by zero is not defined. Multiply both sides of the equation by 3\left(8a-5\right), the least common multiple of 8a-5,3.

$$3\left(a+7\right)=2\left(8a-5\right)$$

Use the distributive property to multiply 3 by a+7.

$$3a+21=2\left(8a-5\right)$$

Use the distributive property to multiply 2 by 8a-5.

$$3a+21=16a-10$$

Subtract 16a from both sides.

$$3a+21-16a=-10$$

Combine 3a and -16a to get -13a.

$$-13a+21=-10$$

Subtract 21 from both sides.

$$-13a=-10-21$$

Subtract 21 from -10 to get -31.

$$-13a=-31$$

Divide both sides by -13.

$$a=\frac{-31}{-13}$$

Fraction \frac{-31}{-13} can be simplified to \frac{31}{13} by removing the negative sign from both the numerator and the denominator.

$$a=\frac{31}{13}$$