Solve x+2<5left(2x+8right)+13(4-x)

$$x+2 < 5 \left( 2x+8 \right) +13(4-x)$$

Solve for x

$$x<\frac{45}{2}$$

Solution Steps

Use the distributive property to multiply 5 by 2x+8.

$$x+2<10x+40+13\left(4-x\right)$$

Use the distributive property to multiply 13 by 4-x.

$$x+2<10x+40+52-13x$$

Add 40 and 52 to get 92.

$$x+2<10x+92-13x$$

Combine 10x and -13x to get -3x.

$$x+2<-3x+92$$

Add 3x to both sides.

$$x+2+3x<92$$

Combine x and 3x to get 4x.

$$4x+2<92$$

Subtract 2 from both sides.

$$4x<92-2$$

Subtract 2 from 92 to get 90.

$$4x<90$$

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

$$x<\frac{90}{4}$$

Reduce the fraction \frac{90}{4} to lowest terms by extracting and canceling out 2.

$$x<\frac{45}{2}$$