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

$$3 ( x - 5 ) + 3 x + 1 = 2 ( x - 2 ) + 15 ( x - 3 )$$

Solve for x

$$x = \frac{35}{11} = 3\frac{2}{11} \approx 3.181818182$$

Steps for Solving Linear Equation

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

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

Combine 3x and 3x to get 6x.

$$6x-15+1=2\left(x-2\right)+15\left(x-3\right)$$

Add -15 and 1 to get -14.

$$6x-14=2\left(x-2\right)+15\left(x-3\right)$$

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

$$6x-14=2x-4+15\left(x-3\right)$$

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

$$6x-14=2x-4+15x-45$$

Combine 2x and 15x to get 17x.

$$6x-14=17x-4-45$$

Subtract 45 from -4 to get -49.

$$6x-14=17x-49$$

Subtract 17x from both sides.

$$6x-14-17x=-49$$

Combine 6x and -17x to get -11x.

$$-11x-14=-49$$

Add 14 to both sides.

$$-11x=-49+14$$

Add -49 and 14 to get -35.

$$-11x=-35$$

Divide both sides by -11.

$$x=\frac{-35}{-11}$$

Fraction \frac{-35}{-11} can be simplified to \frac{35}{11} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{35}{11}$$