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

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

Solve for x

$$x=-1.8$$

Steps for Solving Linear Equation

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

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

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

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

Combine 3.4x and -2.4x to get x.

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

Add -3.4 and 2.4 to get -1.

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

Multiply 7 and 0.5 to get 3.5.

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

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

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

Add 3.5 and 4.5 to get 8.

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

Subtract 6x from both sides.

$$x-1-6x=8$$

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

$$-5x-1=8$$

Add 1 to both sides.

$$-5x=8+1$$

Add 8 and 1 to get 9.

$$-5x=9$$

Divide both sides by -5.

$$x=\frac{9}{-5}$$

Fraction \frac{9}{-5} can be rewritten as -\frac{9}{5} by extracting the negative sign.

$$x=-\frac{9}{5}$$