Solve -[2(3x-3)-(1+x)]-[5(3-2x)-(1+x)]=0

$$- [ 2 ( 3 x - 3 ) - ( 1 + x ) ] - [ 5 ( 3 - 2 x ) - ( 1 + x ) ] = 0$$

Solve for x

$$x = \frac{7}{6} = 1\frac{1}{6} \approx 1.166666667$$

Steps for Solving Linear Equation

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

$$-\left(6x-6-\left(1+x\right)\right)-\left(5\left(3-2x\right)-\left(1+x\right)\right)=0$$

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

$$-\left(6x-6-1-x\right)-\left(5\left(3-2x\right)-\left(1+x\right)\right)=0$$

Subtract 1 from -6 to get -7.

$$-\left(6x-7-x\right)-\left(5\left(3-2x\right)-\left(1+x\right)\right)=0$$

Combine 6x and -x to get 5x.

$$-\left(5x-7\right)-\left(5\left(3-2x\right)-\left(1+x\right)\right)=0$$

To find the opposite of 5x-7, find the opposite of each term.

$$-5x-\left(-7\right)-\left(5\left(3-2x\right)-\left(1+x\right)\right)=0$$

The opposite of -7 is 7.

$$-5x+7-\left(5\left(3-2x\right)-\left(1+x\right)\right)=0$$

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

$$-5x+7-\left(15-10x-\left(1+x\right)\right)=0$$

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

$$-5x+7-\left(15-10x-1-x\right)=0$$

Subtract 1 from 15 to get 14.

$$-5x+7-\left(14-10x-x\right)=0$$

Combine -10x and -x to get -11x.

$$-5x+7-\left(14-11x\right)=0$$

To find the opposite of 14-11x, find the opposite of each term.

$$-5x+7-14-\left(-11x\right)=0$$

The opposite of -11x is 11x.

$$-5x+7-14+11x=0$$

Subtract 14 from 7 to get -7.

$$-5x-7+11x=0$$

Combine -5x and 11x to get 6x.

$$6x-7=0$$

Add 7 to both sides. Anything plus zero gives itself.

$$6x=7$$

Divide both sides by 6.

$$x=\frac{7}{6}$$