Solve 2/3(6a-9)=1/2(4a+8)

$$\frac { 2 } { 3 } ( 6 a - 9 ) = \frac { 1 } { 2 } ( 4 a + 8 )$$

Solve for a

$$a=5$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{3} by 6a-9.

$$\frac{2}{3}\times 6a+\frac{2}{3}\left(-9\right)=\frac{1}{2}\left(4a+8\right)$$

Express \frac{2}{3}\times 6 as a single fraction.

$$\frac{2\times 6}{3}a+\frac{2}{3}\left(-9\right)=\frac{1}{2}\left(4a+8\right)$$

Multiply 2 and 6 to get 12.

$$\frac{12}{3}a+\frac{2}{3}\left(-9\right)=\frac{1}{2}\left(4a+8\right)$$

Divide 12 by 3 to get 4.

$$4a+\frac{2}{3}\left(-9\right)=\frac{1}{2}\left(4a+8\right)$$

Express \frac{2}{3}\left(-9\right) as a single fraction.

$$4a+\frac{2\left(-9\right)}{3}=\frac{1}{2}\left(4a+8\right)$$

Multiply 2 and -9 to get -18.

$$4a+\frac{-18}{3}=\frac{1}{2}\left(4a+8\right)$$

Divide -18 by 3 to get -6.

$$4a-6=\frac{1}{2}\left(4a+8\right)$$

Use the distributive property to multiply \frac{1}{2} by 4a+8.

$$4a-6=\frac{1}{2}\times 4a+\frac{1}{2}\times 8$$

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

$$4a-6=\frac{4}{2}a+\frac{1}{2}\times 8$$

Divide 4 by 2 to get 2.

$$4a-6=2a+\frac{1}{2}\times 8$$

Multiply \frac{1}{2} and 8 to get \frac{8}{2}.

$$4a-6=2a+\frac{8}{2}$$

Divide 8 by 2 to get 4.

$$4a-6=2a+4$$

Subtract 2a from both sides.

$$4a-6-2a=4$$

Combine 4a and -2a to get 2a.

$$2a-6=4$$

Add 6 to both sides.

$$2a=4+6$$

Add 4 and 6 to get 10.

$$2a=10$$

Divide both sides by 2.

$$a=\frac{10}{2}$$

Divide 10 by 2 to get 5.

$$a=5$$