Solve 8(x+10)-9<75+10(1+x)

$$8 ( x + 10 ) - 9 < 75 + 10 ( 1 + x )$$

Solve for x

$$x>-7$$

Solution Steps

Use the distributive property to multiply 8 by x+10.

$$8x+80-9<75+10\left(1+x\right)$$

Subtract 9 from 80 to get 71.

$$8x+71<75+10\left(1+x\right)$$

Use the distributive property to multiply 10 by 1+x.

$$8x+71<75+10+10x$$

Add 75 and 10 to get 85.

$$8x+71<85+10x$$

Subtract 10x from both sides.

$$8x+71-10x<85$$

Combine 8x and -10x to get -2x.

$$-2x+71<85$$

Subtract 71 from both sides.

$$-2x<85-71$$

Subtract 71 from 85 to get 14.

$$-2x<14$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$x>\frac{14}{-2}$$

Divide 14 by -2 to get -7.

$$x>-7$$