Solve 2+3[x-(3x+1)]=5[x-(2x-1)]*e

$$2 + 3 [ x - ( 3 x + 1 ) ] = 5 [ x - ( 2 x - 1 ) ] \cdot e$$

Solve for x

$$x=\frac{5e+1}{5e-6}\approx 1.922094946$$

Steps for Solving Linear Equation

To find the opposite of 3x+1, find the opposite of each term.

$$2+3\left(x-3x-1\right)=5\left(x-\left(2x-1\right)\right)e$$

Combine x and -3x to get -2x.

$$2+3\left(-2x-1\right)=5\left(x-\left(2x-1\right)\right)e$$

Use the distributive property to multiply 3 by -2x-1.

$$2-6x-3=5\left(x-\left(2x-1\right)\right)e$$

Subtract 3 from 2 to get -1.

$$-1-6x=5\left(x-\left(2x-1\right)\right)e$$

To find the opposite of 2x-1, find the opposite of each term.

$$-1-6x=5\left(x-2x-\left(-1\right)\right)e$$

The opposite of -1 is 1.

$$-1-6x=5\left(x-2x+1\right)e$$

Combine x and -2x to get -x.

$$-1-6x=5\left(-x+1\right)e$$

Use the distributive property to multiply 5 by -x+1.

$$-1-6x=\left(-5x+5\right)e$$

Use the distributive property to multiply -5x+5 by e.

$$-1-6x=-5xe+5e$$

Add 5xe to both sides.

$$-1-6x+5xe=5e$$

Add 1 to both sides.

$$-6x+5xe=5e+1$$

Combine all terms containing x.

$$\left(-6+5e\right)x=5e+1$$

The equation is in standard form.

$$\left(5e-6\right)x=5e+1$$

Divide both sides by -6+5e.

$$\frac{\left(5e-6\right)x}{5e-6}=\frac{5e+1}{5e-6}$$

Dividing by -6+5e undoes the multiplication by -6+5e.

$$x=\frac{5e+1}{5e-6}$$