Solve (3x-2)H-7=(4x-5)(5-22)

$$( 3 x - 2 ) H - 7 = ( 4 x - 5 ) ( 5 - 22 )$$

Solve for H

$$H=-\frac{4\left(17x-23\right)}{3x-2}$$

$$x\neq \frac{2}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3x-2 by H.

$$3xH-2H-7=\left(4x-5\right)\left(5-22\right)$$

Subtract 22 from 5 to get -17.

$$3xH-2H-7=\left(4x-5\right)\left(-17\right)$$

Use the distributive property to multiply 4x-5 by -17.

$$3xH-2H-7=-68x+85$$

Add 7 to both sides.

$$3xH-2H=-68x+85+7$$

Add 85 and 7 to get 92.

$$3xH-2H=-68x+92$$

Combine all terms containing H.

$$\left(3x-2\right)H=-68x+92$$

The equation is in standard form.

$$\left(3x-2\right)H=92-68x$$

Divide both sides by 3x-2.

$$\frac{\left(3x-2\right)H}{3x-2}=\frac{92-68x}{3x-2}$$

Dividing by 3x-2 undoes the multiplication by 3x-2.

$$H=\frac{92-68x}{3x-2}$$

Divide -68x+92 by 3x-2.

$$H=\frac{4\left(23-17x\right)}{3x-2}$$

Solve for x

$$x=\frac{2\left(H+46\right)}{3H+68}$$

$$H\neq -\frac{68}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3x-2 by H.

$$3xH-2H-7=\left(4x-5\right)\left(5-22\right)$$

Subtract 22 from 5 to get -17.

$$3xH-2H-7=\left(4x-5\right)\left(-17\right)$$

Use the distributive property to multiply 4x-5 by -17.

$$3xH-2H-7=-68x+85$$

Add 68x to both sides.

$$3xH-2H-7+68x=85$$

Add 2H to both sides.

$$3xH-7+68x=85+2H$$

Add 7 to both sides.

$$3xH+68x=85+2H+7$$

Add 85 and 7 to get 92.

$$3xH+68x=92+2H$$

Combine all terms containing x.

$$\left(3H+68\right)x=92+2H$$

The equation is in standard form.

$$\left(3H+68\right)x=2H+92$$

Divide both sides by 68+3H.

$$\frac{\left(3H+68\right)x}{3H+68}=\frac{2H+92}{3H+68}$$

Dividing by 68+3H undoes the multiplication by 68+3H.

$$x=\frac{2H+92}{3H+68}$$

Divide 92+2H by 68+3H.

$$x=\frac{2\left(H+46\right)}{3H+68}$$