Solve -1/3(-6-9x)+100x-(x+1)=3(33x+4)-2

$$- \frac { 1 } { 3 } ( - 6 - 9 x ) + 100 x - ( x + 1 ) = 3 ( 33 x + 4 ) - 2$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{1}{3} by -6-9x.

$$-\frac{1}{3}\left(-6\right)-\frac{1}{3}\left(-9\right)x+100x-\left(x+1\right)=3\left(33x+4\right)-2$$

Express -\frac{1}{3}\left(-6\right) as a single fraction.

$$\frac{-\left(-6\right)}{3}-\frac{1}{3}\left(-9\right)x+100x-\left(x+1\right)=3\left(33x+4\right)-2$$

Multiply -1 and -6 to get 6.

$$\frac{6}{3}-\frac{1}{3}\left(-9\right)x+100x-\left(x+1\right)=3\left(33x+4\right)-2$$

Divide 6 by 3 to get 2.

$$2-\frac{1}{3}\left(-9\right)x+100x-\left(x+1\right)=3\left(33x+4\right)-2$$

Express -\frac{1}{3}\left(-9\right) as a single fraction.

$$2+\frac{-\left(-9\right)}{3}x+100x-\left(x+1\right)=3\left(33x+4\right)-2$$

Multiply -1 and -9 to get 9.

$$2+\frac{9}{3}x+100x-\left(x+1\right)=3\left(33x+4\right)-2$$

Divide 9 by 3 to get 3.

$$2+3x+100x-\left(x+1\right)=3\left(33x+4\right)-2$$

Combine 3x and 100x to get 103x.

$$2+103x-\left(x+1\right)=3\left(33x+4\right)-2$$

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

$$2+103x-x-1=3\left(33x+4\right)-2$$

Combine 103x and -x to get 102x.

$$2+102x-1=3\left(33x+4\right)-2$$

Subtract 1 from 2 to get 1.

$$1+102x=3\left(33x+4\right)-2$$

Use the distributive property to multiply 3 by 33x+4.

$$1+102x=99x+12-2$$

Subtract 2 from 12 to get 10.

$$1+102x=99x+10$$

Subtract 99x from both sides.

$$1+102x-99x=10$$

Combine 102x and -99x to get 3x.

$$1+3x=10$$

Subtract 1 from both sides.

$$3x=10-1$$

Subtract 1 from 10 to get 9.

$$3x=9$$

Divide both sides by 3.

$$x=\frac{9}{3}$$

Divide 9 by 3 to get 3.

$$x=3$$