Solve 2(x-2)+3(x-3)=3(x-5)-4(x-8)

$$2 ( x - 2 ) + 3 ( x - 3 ) = 3 ( x - 5 ) - 4 ( x - 8 )$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

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

$$2x-4+3\left(x-3\right)=3\left(x-5\right)-4\left(x-8\right)$$

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

$$2x-4+3x-9=3\left(x-5\right)-4\left(x-8\right)$$

Combine 2x and 3x to get 5x.

$$5x-4-9=3\left(x-5\right)-4\left(x-8\right)$$

Subtract 9 from -4 to get -13.

$$5x-13=3\left(x-5\right)-4\left(x-8\right)$$

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

$$5x-13=3x-15-4\left(x-8\right)$$

Use the distributive property to multiply -4 by x-8.

$$5x-13=3x-15-4x+32$$

Combine 3x and -4x to get -x.

$$5x-13=-x-15+32$$

Add -15 and 32 to get 17.

$$5x-13=-x+17$$

Add x to both sides.

$$5x-13+x=17$$

Combine 5x and x to get 6x.

$$6x-13=17$$

Add 13 to both sides.

$$6x=17+13$$

Add 17 and 13 to get 30.

$$6x=30$$

Divide both sides by 6.

$$x=\frac{30}{6}$$

Divide 30 by 6 to get 5.

$$x=5$$