Solve 2(x-5)+3(x-2)=8+7(x-4)

$$2 ( x - 5 ) + 3 ( x - 2 ) = 8 + 7 ( x - 4 )$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by x-5.

$$2x-10+3\left(x-2\right)=8+7\left(x-4\right)$$

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

$$2x-10+3x-6=8+7\left(x-4\right)$$

Combine 2x and 3x to get 5x.

$$5x-10-6=8+7\left(x-4\right)$$

Subtract 6 from -10 to get -16.

$$5x-16=8+7\left(x-4\right)$$

Use the distributive property to multiply 7 by x-4.

$$5x-16=8+7x-28$$

Subtract 28 from 8 to get -20.

$$5x-16=-20+7x$$

Subtract 7x from both sides.

$$5x-16-7x=-20$$

Combine 5x and -7x to get -2x.

$$-2x-16=-20$$

Add 16 to both sides.

$$-2x=-20+16$$

Add -20 and 16 to get -4.

$$-2x=-4$$

Divide both sides by -2.

$$x=\frac{-4}{-2}$$

Divide -4 by -2 to get 2.

$$x=2$$