Solve (2+a):(6a-8)=3:2

$$( 2 + a ) : ( 6 a - 8 ) = 3 : 2$$

Solve for a

$$a = \frac{7}{4} = 1\frac{3}{4} = 1.75$$

Steps for Solving Linear Equation

Variable a cannot be equal to \frac{4}{3} since division by zero is not defined. Multiply both sides of the equation by 2\left(3a-4\right), the least common multiple of 6a-8,2.

$$2+a=3\left(3a-4\right)$$

Use the distributive property to multiply 3 by 3a-4.

$$2+a=9a-12$$

Subtract 9a from both sides.

$$2+a-9a=-12$$

Combine a and -9a to get -8a.

$$2-8a=-12$$

Subtract 2 from both sides.

$$-8a=-12-2$$

Subtract 2 from -12 to get -14.

$$-8a=-14$$

Divide both sides by -8.

$$a=\frac{-14}{-8}$$

Reduce the fraction \frac{-14}{-8} to lowest terms by extracting and canceling out -2.

$$a=\frac{7}{4}$$