Solve 11h-(5-3h)-h-7(4h-3)=-h-(-52-h)

$$11 h - ( 5 - 3 h ) - h - 7 ( 4 h - 3 ) = - h - ( - 52 - h )$$

Solve for h

$$h = -\frac{12}{5} = -2\frac{2}{5} = -2.4$$

Steps for Solving Linear Equation

To find the opposite of 5-3h, find the opposite of each term.

$$11h-5-\left(-3h\right)-h-7\left(4h-3\right)=-h-\left(-52-h\right)$$

The opposite of -3h is 3h.

$$11h-5+3h-h-7\left(4h-3\right)=-h-\left(-52-h\right)$$

Combine 11h and 3h to get 14h.

$$14h-5-h-7\left(4h-3\right)=-h-\left(-52-h\right)$$

Combine 14h and -h to get 13h.

$$13h-5-7\left(4h-3\right)=-h-\left(-52-h\right)$$

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

$$13h-5-28h+21=-h-\left(-52-h\right)$$

Combine 13h and -28h to get -15h.

$$-15h-5+21=-h-\left(-52-h\right)$$

Add -5 and 21 to get 16.

$$-15h+16=-h-\left(-52-h\right)$$

To find the opposite of -52-h, find the opposite of each term.

$$-15h+16=-h-\left(-52\right)-\left(-h\right)$$

The opposite of -52 is 52.

$$-15h+16=-h+52-\left(-h\right)$$

The opposite of -h is h.

$$-15h+16=-h+52+h$$

Add h to both sides.

$$-15h+16+h=52+h$$

Combine -15h and h to get -14h.

$$-14h+16=52+h$$

Subtract h from both sides.

$$-14h+16-h=52$$

Combine -14h and -h to get -15h.

$$-15h+16=52$$

Subtract 16 from both sides.

$$-15h=52-16$$

Subtract 16 from 52 to get 36.

$$-15h=36$$

Divide both sides by -15.

$$h=\frac{36}{-15}$$

Reduce the fraction \frac{36}{-15} to lowest terms by extracting and canceling out 3.

$$h=-\frac{12}{5}$$