Solve 3.4(x-1)-1.2(2x-2)=7(0.5-x)+2(2.25+3x)

$$3.4(x-1)-1.2(2x-2)=7(0.5-x)+2(2.25+3x)$$

Solve for x

$$x=4.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3.4 by x-1.

$$3.4x-3.4-1.2\left(2x-2\right)=7\left(0.5-x\right)+2\left(2.25+3x\right)$$

Use the distributive property to multiply -1.2 by 2x-2.

$$3.4x-3.4-2.4x+2.4=7\left(0.5-x\right)+2\left(2.25+3x\right)$$

Combine 3.4x and -2.4x to get x.

$$x-3.4+2.4=7\left(0.5-x\right)+2\left(2.25+3x\right)$$

Add -3.4 and 2.4 to get -1.

$$x-1=7\left(0.5-x\right)+2\left(2.25+3x\right)$$

Use the distributive property to multiply 7 by 0.5-x.

$$x-1=3.5-7x+2\left(2.25+3x\right)$$

Use the distributive property to multiply 2 by 2.25+3x.

$$x-1=3.5-7x+4.5+6x$$

Add 3.5 and 4.5 to get 8.

$$x-1=8-7x+6x$$

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

$$x-1=8-x$$

Add x to both sides.

$$x-1+x=8$$

Combine x and x to get 2x.

$$2x-1=8$$

Add 1 to both sides.

$$2x=8+1$$

Add 8 and 1 to get 9.

$$2x=9$$

Divide both sides by 2.

$$x=\frac{9}{2}$$