Solve 10g/5*2-15h/5*3=5(2g-3h)

$$\frac { 10 g } { 5 \cdot 2 } - \frac { 15 h } { 5 \cdot 3 } = 5 ( 2 g - 3 h )$$

Solve for g

$$g=\frac{14h}{9}$$

Steps for Solving Linear Equation

Cancel out 2\times 5 in both numerator and denominator.

$$g-\frac{15h}{5\times 3}=5\left(2g-3h\right)$$

Cancel out 3\times 5 in both numerator and denominator.

$$g-h=5\left(2g-3h\right)$$

Use the distributive property to multiply 5 by 2g-3h.

$$g-h=10g-15h$$

Subtract 10g from both sides.

$$g-h-10g=-15h$$

Combine g and -10g to get -9g.

$$-9g-h=-15h$$

Add h to both sides.

$$-9g=-15h+h$$

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

$$-9g=-14h$$

Divide both sides by -9.

$$\frac{-9g}{-9}=-\frac{14h}{-9}$$

Dividing by -9 undoes the multiplication by -9.

$$g=-\frac{14h}{-9}$$

Divide -14h by -9.

$$g=\frac{14h}{9}$$

Solve for h

$$h=\frac{9g}{14}$$

Steps for Solving Linear Equation

Cancel out 2\times 5 in both numerator and denominator.

$$g-\frac{15h}{5\times 3}=5\left(2g-3h\right)$$

Cancel out 3\times 5 in both numerator and denominator.

$$g-h=5\left(2g-3h\right)$$

Use the distributive property to multiply 5 by 2g-3h.

$$g-h=10g-15h$$

Add 15h to both sides.

$$g-h+15h=10g$$

Subtract g from both sides.

$$-h+15h=10g-g$$

Combine 10g and -g to get 9g.

$$-h+15h=9g$$

Combine -h and 15h to get 14h.

$$14h=9g$$

Divide both sides by 14.

$$\frac{14h}{14}=\frac{9g}{14}$$

Dividing by 14 undoes the multiplication by 14.

$$h=\frac{9g}{14}$$