Solve 4left(x-5right)+3x+1=2left(x-2right)+15left(x-3right)

$$4 \left( x-5 \right) +3x+1 = 2 \left( x-2 \right) +15 \left( x-3 \right)$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by x-5.

$$4x-20+3x+1=2\left(x-2\right)+15\left(x-3\right)$$

Combine 4x and 3x to get 7x.

$$7x-20+1=2\left(x-2\right)+15\left(x-3\right)$$

Add -20 and 1 to get -19.

$$7x-19=2\left(x-2\right)+15\left(x-3\right)$$

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

$$7x-19=2x-4+15\left(x-3\right)$$

Use the distributive property to multiply 15 by x-3.

$$7x-19=2x-4+15x-45$$

Combine 2x and 15x to get 17x.

$$7x-19=17x-4-45$$

Subtract 45 from -4 to get -49.

$$7x-19=17x-49$$

Subtract 17x from both sides.

$$7x-19-17x=-49$$

Combine 7x and -17x to get -10x.

$$-10x-19=-49$$

Add 19 to both sides.

$$-10x=-49+19$$

Add -49 and 19 to get -30.

$$-10x=-30$$

Divide both sides by -10.

$$x=\frac{-30}{-10}$$

Divide -30 by -10 to get 3.

$$x=3$$