Solve 2(2x+1)-3(3x-5)=4(x-5)-8

$$2 ( 2 x + 1 ) - 3 ( 3 x - 5 ) = 4 ( x - 5 ) - 8$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by 2x+1.

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

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

$$4x+2-9x+15=4\left(x-5\right)-8$$

Combine 4x and -9x to get -5x.

$$-5x+2+15=4\left(x-5\right)-8$$

Add 2 and 15 to get 17.

$$-5x+17=4\left(x-5\right)-8$$

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

$$-5x+17=4x-20-8$$

Subtract 8 from -20 to get -28.

$$-5x+17=4x-28$$

Subtract 4x from both sides.

$$-5x+17-4x=-28$$

Combine -5x and -4x to get -9x.

$$-9x+17=-28$$

Subtract 17 from both sides.

$$-9x=-28-17$$

Subtract 17 from -28 to get -45.

$$-9x=-45$$

Divide both sides by -9.

$$x=\frac{-45}{-9}$$

Divide -45 by -9 to get 5.

$$x=5$$