Solve 7(3a-4)-3(4a+5)-(6a+2)=a+8(4a-9)+1

$$7 ( 3 a - 4 ) - 3 ( 4 a + 5 ) - ( 6 a + 2 ) = a + 8 ( 4 a - 9 ) + 1$$

Solve for a

$$a=\frac{13}{15}\approx 0.866666667$$

Steps for Solving Linear Equation

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

$$21a-28-3\left(4a+5\right)-\left(6a+2\right)=a+8\left(4a-9\right)+1$$

Use the distributive property to multiply -3 by 4a+5.

$$21a-28-12a-15-\left(6a+2\right)=a+8\left(4a-9\right)+1$$

Combine 21a and -12a to get 9a.

$$9a-28-15-\left(6a+2\right)=a+8\left(4a-9\right)+1$$

Subtract 15 from -28 to get -43.

$$9a-43-\left(6a+2\right)=a+8\left(4a-9\right)+1$$

To find the opposite of 6a+2, find the opposite of each term.

$$9a-43-6a-2=a+8\left(4a-9\right)+1$$

Combine 9a and -6a to get 3a.

$$3a-43-2=a+8\left(4a-9\right)+1$$

Subtract 2 from -43 to get -45.

$$3a-45=a+8\left(4a-9\right)+1$$

Use the distributive property to multiply 8 by 4a-9.

$$3a-45=a+32a-72+1$$

Combine a and 32a to get 33a.

$$3a-45=33a-72+1$$

Add -72 and 1 to get -71.

$$3a-45=33a-71$$

Subtract 33a from both sides.

$$3a-45-33a=-71$$

Combine 3a and -33a to get -30a.

$$-30a-45=-71$$

Add 45 to both sides.

$$-30a=-71+45$$

Add -71 and 45 to get -26.

$$-30a=-26$$

Divide both sides by -30.

$$a=\frac{-26}{-30}$$

Reduce the fraction \frac{-26}{-30} to lowest terms by extracting and canceling out -2.

$$a=\frac{13}{15}$$