Solve 7(4a-3)-(2a+1)*9=2(a-9)

$$7 ( 4 a - 3 ) - ( 2 a + 1 ) \cdot 9 = 2 ( a - 9 )$$

Solve for a

$$a = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply 7 by 4a-3.

$$28a-21-\left(2a+1\right)\times 9=2\left(a-9\right)$$

Use the distributive property to multiply 2a+1 by 9.

$$28a-21-\left(18a+9\right)=2\left(a-9\right)$$

To find the opposite of 18a+9, find the opposite of each term.

$$28a-21-18a-9=2\left(a-9\right)$$

Combine 28a and -18a to get 10a.

$$10a-21-9=2\left(a-9\right)$$

Subtract 9 from -21 to get -30.

$$10a-30=2\left(a-9\right)$$

Use the distributive property to multiply 2 by a-9.

$$10a-30=2a-18$$

Subtract 2a from both sides.

$$10a-30-2a=-18$$

Combine 10a and -2a to get 8a.

$$8a-30=-18$$

Add 30 to both sides.

$$8a=-18+30$$

Add -18 and 30 to get 12.

$$8a=12$$

Divide both sides by 8.

$$a=\frac{12}{8}$$

Reduce the fraction \frac{12}{8} to lowest terms by extracting and canceling out 4.

$$a=\frac{3}{2}$$