Solve f(x)=4x+2quadg(x)=x/4-1/2

$$f ( x ) = 4 x + 2 \quad g ( x ) = \frac { x } { 4 } - \frac { 1 } { 2 }$$

Solve for g

$$g=-\frac{15}{8}-\frac{1}{4x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$16x+8gx=x-2$$

Subtract 16x from both sides.

$$8gx=x-2-16x$$

Combine x and -16x to get -15x.

$$8gx=-15x-2$$

The equation is in standard form.

$$8xg=-15x-2$$

Divide both sides by 8x.

$$\frac{8xg}{8x}=\frac{-15x-2}{8x}$$

Dividing by 8x undoes the multiplication by 8x.

$$g=\frac{-15x-2}{8x}$$

Divide -15x-2 by 8x.

$$g=-\frac{15}{8}-\frac{1}{4x}$$

Solve for x

$$x=-\frac{2}{8g+15}$$

$$g\neq -\frac{15}{8}$$

Steps for Solving Linear Equation

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

$$16x+8gx=x-2$$

Subtract x from both sides.

$$16x+8gx-x=-2$$

Combine 16x and -x to get 15x.

$$15x+8gx=-2$$

Combine all terms containing x.

$$\left(15+8g\right)x=-2$$

The equation is in standard form.

$$\left(8g+15\right)x=-2$$

Divide both sides by 15+8g.

$$\frac{\left(8g+15\right)x}{8g+15}=-\frac{2}{8g+15}$$

Dividing by 15+8g undoes the multiplication by 15+8g.

$$x=-\frac{2}{8g+15}$$