Solve 8(x+10)-14<54+10(2+x)

$$8 ( x + 10 ) - 14 < 54 + 10 ( 2 + x )$$

Solve for x

$$x>-4$$

Solution Steps

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

$$8x+80-14<54+10\left(2+x\right)$$

Subtract 14 from 80 to get 66.

$$8x+66<54+10\left(2+x\right)$$

Use the distributive property to multiply 10 by 2+x.

$$8x+66<54+20+10x$$

Add 54 and 20 to get 74.

$$8x+66<74+10x$$

Subtract 10x from both sides.

$$8x+66-10x<74$$

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

$$-2x+66<74$$

Subtract 66 from both sides.

$$-2x<74-66$$

Subtract 66 from 74 to get 8.

$$-2x<8$$

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

$$x>\frac{8}{-2}$$

Divide 8 by -2 to get -4.

$$x>-4$$