Solve 24(3x+1)-(2x-5)+16=2(3x+1)+(2x-5)

$$24 ( 3 x + 1 ) - ( 2 x - 5 ) + 16 = 2 ( 3 x + 1 ) + ( 2 x - 5 )$$

Solve for x

$$x=-\frac{24}{31}\approx -0.774193548$$

Steps for Solving Linear Equation

Use the distributive property to multiply 24 by 3x+1.

$$72x+24-\left(2x-5\right)+16=2\left(3x+1\right)+2x-5$$

To find the opposite of 2x-5, find the opposite of each term.

$$72x+24-2x-\left(-5\right)+16=2\left(3x+1\right)+2x-5$$

The opposite of -5 is 5.

$$72x+24-2x+5+16=2\left(3x+1\right)+2x-5$$

Combine 72x and -2x to get 70x.

$$70x+24+5+16=2\left(3x+1\right)+2x-5$$

Add 24 and 5 to get 29.

$$70x+29+16=2\left(3x+1\right)+2x-5$$

Add 29 and 16 to get 45.

$$70x+45=2\left(3x+1\right)+2x-5$$

Use the distributive property to multiply 2 by 3x+1.

$$70x+45=6x+2+2x-5$$

Combine 6x and 2x to get 8x.

$$70x+45=8x+2-5$$

Subtract 5 from 2 to get -3.

$$70x+45=8x-3$$

Subtract 8x from both sides.

$$70x+45-8x=-3$$

Combine 70x and -8x to get 62x.

$$62x+45=-3$$

Subtract 45 from both sides.

$$62x=-3-45$$

Subtract 45 from -3 to get -48.

$$62x=-48$$

Divide both sides by 62.

$$x=\frac{-48}{62}$$

Reduce the fraction \frac{-48}{62} to lowest terms by extracting and canceling out 2.

$$x=-\frac{24}{31}$$