Solve 2400-120x-8ax+4x=500

$$2400 - 120 x - 8 a x + 4 x = 500$$

Solve for a

$$a=-\frac{29}{2}+\frac{475}{2x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Combine -120x and 4x to get -116x.

$$2400-116x-8ax=500$$

Subtract 2400 from both sides.

$$-116x-8ax=500-2400$$

Subtract 2400 from 500 to get -1900.

$$-116x-8ax=-1900$$

Add 116x to both sides.

$$-8ax=-1900+116x$$

The equation is in standard form.

$$\left(-8x\right)a=116x-1900$$

Divide both sides by -8x.

$$\frac{\left(-8x\right)a}{-8x}=\frac{116x-1900}{-8x}$$

Dividing by -8x undoes the multiplication by -8x.

$$a=\frac{116x-1900}{-8x}$$

Divide -1900+116x by -8x.

$$a=-\frac{29}{2}+\frac{475}{2x}$$

Solve for x

$$x=\frac{475}{2a+29}$$

$$a\neq -\frac{29}{2}$$

Steps for Solving Linear Equation

Combine -120x and 4x to get -116x.

$$2400-116x-8ax=500$$

Subtract 2400 from both sides.

$$-116x-8ax=500-2400$$

Subtract 2400 from 500 to get -1900.

$$-116x-8ax=-1900$$

Combine all terms containing x.

$$\left(-116-8a\right)x=-1900$$

The equation is in standard form.

$$\left(-8a-116\right)x=-1900$$

Divide both sides by -116-8a.

$$\frac{\left(-8a-116\right)x}{-8a-116}=-\frac{1900}{-8a-116}$$

Dividing by -116-8a undoes the multiplication by -116-8a.

$$x=-\frac{1900}{-8a-116}$$

Divide -1900 by -116-8a.

$$x=\frac{475}{2a+29}$$