Solve 4x-11-(x-6)=3(x-1)-2

$$4x-11-(x-6)=3(x-1)-2$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

Solution Steps

To find the opposite of x-6, find the opposite of each term.

$$4x-11-x-\left(-6\right)=3\left(x-1\right)-2$$

The opposite of -6 is 6.

$$4x-11-x+6=3\left(x-1\right)-2$$

Combine 4x and -x to get 3x.

$$3x-11+6=3\left(x-1\right)-2$$

Add -11 and 6 to get -5.

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

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

$$3x-5=3x-3-2$$

Subtract 2 from -3 to get -5.

$$3x-5=3x-5$$

Subtract 3x from both sides.

$$3x-5-3x=-5$$

Combine 3x and -3x to get 0.

$$-5=-5$$

Compare -5 and -5.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

To find the opposite of x-6, find the opposite of each term.

$$4x-11-x-\left(-6\right)=3\left(x-1\right)-2$$

The opposite of -6 is 6.

$$4x-11-x+6=3\left(x-1\right)-2$$

Combine 4x and -x to get 3x.

$$3x-11+6=3\left(x-1\right)-2$$

Add -11 and 6 to get -5.

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

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

$$3x-5=3x-3-2$$

Subtract 2 from -3 to get -5.

$$3x-5=3x-5$$

Subtract 3x from both sides.

$$3x-5-3x=-5$$

Combine 3x and -3x to get 0.

$$-5=-5$$

Compare -5 and -5.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$