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

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

Solve for x

$$x = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

Steps for Solving Linear Equation

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

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

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

$$3x-6=5x-15$$

Subtract 5x from both sides.

$$3x-6-5x=-15$$

Combine 3x and -5x to get -2x.

$$-2x-6=-15$$

Add 6 to both sides.

$$-2x=-15+6$$

Add -15 and 6 to get -9.

$$-2x=-9$$

Divide both sides by -2.

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

Fraction \frac{-9}{-2} can be simplified to \frac{9}{2} by removing the negative sign from both the numerator and the denominator.

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