Solve 3(2x-5)=2(15-x)-1operatorname{es}x

$$3 ( 2 x - 5 ) = 2 ( 15 - x ) - 1 \operatorname { es } x$$

Solve for s

$$s=\frac{45-8x}{ex}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$6x-15=2\left(15-x\right)-1esx$$

Use the distributive property to multiply 2 by 15-x.

$$6x-15=30-2x-1esx$$

Swap sides so that all variable terms are on the left hand side.

$$30-2x-1esx=6x-15$$

Reorder the terms.

$$-2x+30-esx=6x-15$$

Add 2x to both sides.

$$30-esx=6x-15+2x$$

Combine 6x and 2x to get 8x.

$$30-esx=8x-15$$

Subtract 30 from both sides.

$$-esx=8x-15-30$$

Subtract 30 from -15 to get -45.

$$-esx=8x-45$$

The equation is in standard form.

$$\left(-ex\right)s=8x-45$$

Divide both sides by -ex.

$$\frac{\left(-ex\right)s}{-ex}=\frac{8x-45}{-ex}$$

Dividing by -ex undoes the multiplication by -ex.

$$s=\frac{8x-45}{-ex}$$

Divide 8x-45 by -ex.

$$s=\frac{45-8x}{ex}$$

Solve for x

$$x=\frac{45}{es+8}$$

$$s\neq -\frac{8}{e}$$

Steps for Solving Linear Equation

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

$$6x-15=2\left(15-x\right)-1esx$$

Use the distributive property to multiply 2 by 15-x.

$$6x-15=30-2x-1esx$$

Add 1esx to both sides.

$$6x-15+1esx=30-2x$$

Add 2x to both sides.

$$6x-15+1esx+2x=30$$

Combine 6x and 2x to get 8x.

$$8x-15+1esx=30$$

Add 15 to both sides.

$$8x+1esx=30+15$$

Add 30 and 15 to get 45.

$$8x+1esx=45$$

Reorder the terms.

$$esx+8x=45$$

Combine all terms containing x.

$$\left(es+8\right)x=45$$

Divide both sides by 8+es.

$$\frac{\left(es+8\right)x}{es+8}=\frac{45}{es+8}$$

Dividing by 8+es undoes the multiplication by 8+es.

$$x=\frac{45}{es+8}$$