Solve 5(2a+9d)=15/2(2a+14)-10/2(2a+9d)

$$5 ( 2 a + 9 d ) = \frac { 15 } { 2 } ( 2 a + 14 ) - \frac { 10 } { 2 } ( 2 a + 9 d )$$

Solve for a

$$a=21-18d$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by 2a+9d.

$$10a+45d=\frac{15}{2}\left(2a+14\right)-\frac{10}{2}\left(2a+9d\right)$$

Use the distributive property to multiply \frac{15}{2} by 2a+14.

$$10a+45d=15a+105-\frac{10}{2}\left(2a+9d\right)$$

Divide 10 by 2 to get 5.

$$10a+45d=15a+105-5\left(2a+9d\right)$$

Use the distributive property to multiply -5 by 2a+9d.

$$10a+45d=15a+105-10a-45d$$

Combine 15a and -10a to get 5a.

$$10a+45d=5a+105-45d$$

Subtract 5a from both sides.

$$10a+45d-5a=105-45d$$

Combine 10a and -5a to get 5a.

$$5a+45d=105-45d$$

Subtract 45d from both sides.

$$5a=105-45d-45d$$

Combine -45d and -45d to get -90d.

$$5a=105-90d$$

Divide both sides by 5.

$$\frac{5a}{5}=\frac{105-90d}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$a=\frac{105-90d}{5}$$

Divide 105-90d by 5.

$$a=21-18d$$

Solve for d

$$d=-\frac{a}{18}+\frac{7}{6}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by 2a+9d.

$$10a+45d=\frac{15}{2}\left(2a+14\right)-\frac{10}{2}\left(2a+9d\right)$$

Use the distributive property to multiply \frac{15}{2} by 2a+14.

$$10a+45d=15a+105-\frac{10}{2}\left(2a+9d\right)$$

Divide 10 by 2 to get 5.

$$10a+45d=15a+105-5\left(2a+9d\right)$$

Use the distributive property to multiply -5 by 2a+9d.

$$10a+45d=15a+105-10a-45d$$

Combine 15a and -10a to get 5a.

$$10a+45d=5a+105-45d$$

Add 45d to both sides.

$$10a+45d+45d=5a+105$$

Combine 45d and 45d to get 90d.

$$10a+90d=5a+105$$

Subtract 10a from both sides.

$$90d=5a+105-10a$$

Combine 5a and -10a to get -5a.

$$90d=-5a+105$$

The equation is in standard form.

$$90d=105-5a$$

Divide both sides by 90.

$$\frac{90d}{90}=\frac{105-5a}{90}$$

Dividing by 90 undoes the multiplication by 90.

$$d=\frac{105-5a}{90}$$

Divide -5a+105 by 90.

$$d=-\frac{a}{18}+\frac{7}{6}$$