Solve 13(9-2x)-24=7(x+4)+5(11-x)

$$13 ( 9 - 2 x ) - 24 = 7 ( x + 4 ) + 5 ( 11 - x )$$

Solve for x

$$x=\frac{5}{14}\approx 0.357142857$$

Steps for Solving Linear Equation

Use the distributive property to multiply 13 by 9-2x.

$$117-26x-24=7\left(x+4\right)+5\left(11-x\right)$$

Subtract 24 from 117 to get 93.

$$93-26x=7\left(x+4\right)+5\left(11-x\right)$$

Use the distributive property to multiply 7 by x+4.

$$93-26x=7x+28+5\left(11-x\right)$$

Use the distributive property to multiply 5 by 11-x.

$$93-26x=7x+28+55-5x$$

Add 28 and 55 to get 83.

$$93-26x=7x+83-5x$$

Combine 7x and -5x to get 2x.

$$93-26x=2x+83$$

Subtract 2x from both sides.

$$93-26x-2x=83$$

Combine -26x and -2x to get -28x.

$$93-28x=83$$

Subtract 93 from both sides.

$$-28x=83-93$$

Subtract 93 from 83 to get -10.

$$-28x=-10$$

Divide both sides by -28.

$$x=\frac{-10}{-28}$$

Reduce the fraction \frac{-10}{-28} to lowest terms by extracting and canceling out -2.

$$x=\frac{5}{14}$$