Solve 3f-5/7-2f-h/4=-2

$$\frac { 3 f - 5 } { 7 } - \frac { 2 f - h } { 4 } = - 2$$

Solve for f

$$f=\frac{7h}{2}+18$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 28, the least common multiple of 7,4.

$$4\left(3f-5\right)-7\left(2f-h\right)=-56$$

Use the distributive property to multiply 4 by 3f-5.

$$12f-20-7\left(2f-h\right)=-56$$

Use the distributive property to multiply -7 by 2f-h.

$$12f-20-14f+7h=-56$$

Combine 12f and -14f to get -2f.

$$-2f-20+7h=-56$$

Add 20 to both sides.

$$-2f+7h=-56+20$$

Add -56 and 20 to get -36.

$$-2f+7h=-36$$

Subtract 7h from both sides.

$$-2f=-36-7h$$

The equation is in standard form.

$$-2f=-7h-36$$

Divide both sides by -2.

$$\frac{-2f}{-2}=\frac{-7h-36}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$f=\frac{-7h-36}{-2}$$

Divide -36-7h by -2.

$$f=\frac{7h}{2}+18$$

Solve for h

$$h=\frac{2\left(f-18\right)}{7}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 28, the least common multiple of 7,4.

$$4\left(3f-5\right)-7\left(2f-h\right)=-56$$

Use the distributive property to multiply 4 by 3f-5.

$$12f-20-7\left(2f-h\right)=-56$$

Use the distributive property to multiply -7 by 2f-h.

$$12f-20-14f+7h=-56$$

Combine 12f and -14f to get -2f.

$$-2f-20+7h=-56$$

Add 2f to both sides.

$$-20+7h=-56+2f$$

Add 20 to both sides.

$$7h=-56+2f+20$$

Add -56 and 20 to get -36.

$$7h=-36+2f$$

The equation is in standard form.

$$7h=2f-36$$

Divide both sides by 7.

$$\frac{7h}{7}=\frac{2f-36}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$h=\frac{2f-36}{7}$$