Solve 2(4x+5)-3(x-6)=5(3x)+2(5x-3)

$$2(4x+5)-3(x-6)=5(3x)+2(5x-3)$$

Solve for x

$$x = \frac{17}{10} = 1\frac{7}{10} = 1.7$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by 4x+5.

$$8x+10-3\left(x-6\right)=5\times 3x+2\left(5x-3\right)$$

Use the distributive property to multiply -3 by x-6.

$$8x+10-3x+18=5\times 3x+2\left(5x-3\right)$$

Combine 8x and -3x to get 5x.

$$5x+10+18=5\times 3x+2\left(5x-3\right)$$

Add 10 and 18 to get 28.

$$5x+28=5\times 3x+2\left(5x-3\right)$$

Multiply 5 and 3 to get 15.

$$5x+28=15x+2\left(5x-3\right)$$

Use the distributive property to multiply 2 by 5x-3.

$$5x+28=15x+10x-6$$

Combine 15x and 10x to get 25x.

$$5x+28=25x-6$$

Subtract 25x from both sides.

$$5x+28-25x=-6$$

Combine 5x and -25x to get -20x.

$$-20x+28=-6$$

Subtract 28 from both sides.

$$-20x=-6-28$$

Subtract 28 from -6 to get -34.

$$-20x=-34$$

Divide both sides by -20.

$$x=\frac{-34}{-20}$$

Reduce the fraction \frac{-34}{-20} to lowest terms by extracting and canceling out -2.

$$x=\frac{17}{10}$$