Solve 5+frac{u_{1}-u_{0}}{2}-frac{u_{0}}{4}-frac{u_{0}-(-20)}{8}=0

$$5 + \frac { u _ { 1 } - u _ { 0 } } { 2 } - \frac { u _ { 0 } } { 4 } - \frac { u _ { 0 } - ( - 20 ) } { 8 } = 0$$

Solve for u_0

$$u_{0}=\frac{4\left(u_{1}+5\right)}{7}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8, the least common multiple of 2,4,8.

$$40+4\left(u_{1}-u_{0}\right)-2u_{0}-\left(u_{0}-\left(-20\right)\right)=0$$

Use the distributive property to multiply 4 by u_{1}-u_{0}.

$$40+4u_{1}-4u_{0}-2u_{0}-\left(u_{0}-\left(-20\right)\right)=0$$

Combine -4u_{0} and -2u_{0} to get -6u_{0}.

$$40+4u_{1}-6u_{0}-\left(u_{0}-\left(-20\right)\right)=0$$

The opposite of -20 is 20.

$$40+4u_{1}-6u_{0}-\left(u_{0}+20\right)=0$$

To find the opposite of u_{0}+20, find the opposite of each term.

$$40+4u_{1}-6u_{0}-u_{0}-20=0$$

Combine -6u_{0} and -u_{0} to get -7u_{0}.

$$40+4u_{1}-7u_{0}-20=0$$

Subtract 20 from 40 to get 20.

$$20+4u_{1}-7u_{0}=0$$

Subtract 20 from both sides. Anything subtracted from zero gives its negation.

$$4u_{1}-7u_{0}=-20$$

Subtract 4u_{1} from both sides.

$$-7u_{0}=-20-4u_{1}$$

The equation is in standard form.

$$-7u_{0}=-4u_{1}-20$$

Divide both sides by -7.

$$\frac{-7u_{0}}{-7}=\frac{-4u_{1}-20}{-7}$$

Dividing by -7 undoes the multiplication by -7.

$$u_{0}=\frac{-4u_{1}-20}{-7}$$

Divide -20-4u_{1} by -7.

$$u_{0}=\frac{4u_{1}+20}{7}$$

Solve for u_1

$$u_{1}=\frac{7u_{0}}{4}-5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8, the least common multiple of 2,4,8.

$$40+4\left(u_{1}-u_{0}\right)-2u_{0}-\left(u_{0}-\left(-20\right)\right)=0$$

Use the distributive property to multiply 4 by u_{1}-u_{0}.

$$40+4u_{1}-4u_{0}-2u_{0}-\left(u_{0}-\left(-20\right)\right)=0$$

Combine -4u_{0} and -2u_{0} to get -6u_{0}.

$$40+4u_{1}-6u_{0}-\left(u_{0}-\left(-20\right)\right)=0$$

The opposite of -20 is 20.

$$40+4u_{1}-6u_{0}-\left(u_{0}+20\right)=0$$

To find the opposite of u_{0}+20, find the opposite of each term.

$$40+4u_{1}-6u_{0}-u_{0}-20=0$$

Combine -6u_{0} and -u_{0} to get -7u_{0}.

$$40+4u_{1}-7u_{0}-20=0$$

Subtract 20 from 40 to get 20.

$$20+4u_{1}-7u_{0}=0$$

Subtract 20 from both sides. Anything subtracted from zero gives its negation.

$$4u_{1}-7u_{0}=-20$$

Add 7u_{0} to both sides.

$$4u_{1}=-20+7u_{0}$$

The equation is in standard form.

$$4u_{1}=7u_{0}-20$$

Divide both sides by 4.

$$\frac{4u_{1}}{4}=\frac{7u_{0}-20}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$u_{1}=\frac{7u_{0}-20}{4}$$

Divide -20+7u_{0} by 4.

$$u_{1}=\frac{7u_{0}}{4}-5$$