Solve -(8n-2)=3+10(1-3n)

$$- ( 8 n - 2 ) = 3 + 10 ( 1 - 3 n )$$

Solve for n

$$n=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

To find the opposite of 8n-2, find the opposite of each term.

$$-8n-\left(-2\right)=3+10\left(1-3n\right)$$

The opposite of -2 is 2.

$$-8n+2=3+10\left(1-3n\right)$$

Use the distributive property to multiply 10 by 1-3n.

$$-8n+2=3+10-30n$$

Add 3 and 10 to get 13.

$$-8n+2=13-30n$$

Add 30n to both sides.

$$-8n+2+30n=13$$

Combine -8n and 30n to get 22n.

$$22n+2=13$$

Subtract 2 from both sides.

$$22n=13-2$$

Subtract 2 from 13 to get 11.

$$22n=11$$

Divide both sides by 22.

$$n=\frac{11}{22}$$

Reduce the fraction \frac{11}{22} to lowest terms by extracting and canceling out 11.

$$n=\frac{1}{2}$$