Solve 34(x-1)-12(2x-2)=7(05-x)+2(225+3x)

$$34(x-1)-12(2x-2)=7(05-x)+2(225+3x)$$

Solve for x

$$x = \frac{460}{11} = 41\frac{9}{11} \approx 41.818181818$$

Steps for Solving Linear Equation

Use the distributive property to multiply 34 by x-1.

$$34x-34-12\left(2x-2\right)=7\left(0\times 5-x\right)+2\left(225+3x\right)$$

Use the distributive property to multiply -12 by 2x-2.

$$34x-34-24x+24=7\left(0\times 5-x\right)+2\left(225+3x\right)$$

Combine 34x and -24x to get 10x.

$$10x-34+24=7\left(0\times 5-x\right)+2\left(225+3x\right)$$

Add -34 and 24 to get -10.

$$10x-10=7\left(0\times 5-x\right)+2\left(225+3x\right)$$

Multiply 0 and 5 to get 0.

$$10x-10=7\left(0-x\right)+2\left(225+3x\right)$$

Anything plus zero gives itself.

$$10x-10=7\left(-1\right)x+2\left(225+3x\right)$$

Multiply 7 and -1 to get -7.

$$10x-10=-7x+2\left(225+3x\right)$$

Use the distributive property to multiply 2 by 225+3x.

$$10x-10=-7x+450+6x$$

Combine -7x and 6x to get -x.

$$10x-10=-x+450$$

Add x to both sides.

$$10x-10+x=450$$

Combine 10x and x to get 11x.

$$11x-10=450$$

Add 10 to both sides.

$$11x=450+10$$

Add 450 and 10 to get 460.

$$11x=460$$

Divide both sides by 11.

$$x=\frac{460}{11}$$