Solve 3(x-1)+2(2x-3)=5(3x-1)

$$3 ( x - 1 ) + 2 ( 2 x - 3 ) = 5 ( 3 x - 1 )$$

Solve for x

$$x=-\frac{1}{2}=-0.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by x-1.

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

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

$$3x-3+4x-6=5\left(3x-1\right)$$

Combine 3x and 4x to get 7x.

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

Subtract 6 from -3 to get -9.

$$7x-9=5\left(3x-1\right)$$

Use the distributive property to multiply 5 by 3x-1.

$$7x-9=15x-5$$

Subtract 15x from both sides.

$$7x-9-15x=-5$$

Combine 7x and -15x to get -8x.

$$-8x-9=-5$$

Add 9 to both sides.

$$-8x=-5+9$$

Add -5 and 9 to get 4.

$$-8x=4$$

Divide both sides by -8.

$$x=\frac{4}{-8}$$

Reduce the fraction \frac{4}{-8} to lowest terms by extracting and canceling out 4.

$$x=-\frac{1}{2}$$