Solve [17x*15+24*(3ax-15x)/20]-3000=500

$$[ 17 x \cdot 15 + 24 \cdot \frac { ( 3 a x - 15 x ) } { 20 } ] - 3000 = 500$$

Solve for a

$$a=-\frac{395}{6}+\frac{8750}{9x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 20.

$$340x\times 15+24\left(3ax-15x\right)-60000=10000$$

Multiply 340 and 15 to get 5100.

$$5100x+24\left(3ax-15x\right)-60000=10000$$

Use the distributive property to multiply 24 by 3ax-15x.

$$5100x+72xa-360x-60000=10000$$

Combine 5100x and -360x to get 4740x.

$$4740x+72xa-60000=10000$$

Subtract 4740x from both sides.

$$72xa-60000=10000-4740x$$

Add 60000 to both sides.

$$72xa=10000-4740x+60000$$

Add 10000 and 60000 to get 70000.

$$72xa=70000-4740x$$

Divide both sides by 72x.

$$\frac{72xa}{72x}=\frac{70000-4740x}{72x}$$

Dividing by 72x undoes the multiplication by 72x.

$$a=\frac{70000-4740x}{72x}$$

Divide 70000-4740x by 72x.

$$a=-\frac{395}{6}+\frac{8750}{9x}$$

Solve for x

$$x=\frac{17500}{3\left(6a+395\right)}$$

$$a\neq -\frac{395}{6}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 20.

$$340x\times 15+24\left(3ax-15x\right)-60000=10000$$

Multiply 340 and 15 to get 5100.

$$5100x+24\left(3ax-15x\right)-60000=10000$$

Use the distributive property to multiply 24 by 3ax-15x.

$$5100x+72ax-360x-60000=10000$$

Combine 5100x and -360x to get 4740x.

$$4740x+72ax-60000=10000$$

Add 60000 to both sides.

$$4740x+72ax=10000+60000$$

Add 10000 and 60000 to get 70000.

$$4740x+72ax=70000$$

Combine all terms containing x.

$$\left(4740+72a\right)x=70000$$

The equation is in standard form.

$$\left(72a+4740\right)x=70000$$

Divide both sides by 4740+72a.

$$\frac{\left(72a+4740\right)x}{72a+4740}=\frac{70000}{72a+4740}$$

Dividing by 4740+72a undoes the multiplication by 4740+72a.

$$x=\frac{70000}{72a+4740}$$

Divide 70000 by 4740+72a.

$$x=\frac{17500}{3\left(6a+395\right)}$$