# How do you solve and write the following in interval notation: #8x -3x + 2< 2(x + 7)#?

##### 1 Answer

#### Explanation:

We have the inequality

#8x-3x+2 < 2(x+7)#

On the left hand side, the

#overbrace(8x-3x)^(8x-3x=5x)+2 < 2(x+7)#

#5x+2 < 2(x+7)#

Next, on the right hand side, distribute the

#5x+2 < overbrace(2(x+7))^(2(x)+2(7))#

#5x+2 < 2x+14#

Subtract

#overbrace(5x-2x)^(3x)+2 < overbrace(2x-2x)^0+14#

#3x+2 < 14#

Subtract

#3x+overbrace(2-2)^0 < overbrace(14-2)^12#

#3x < 12#

Divide both sides by

#(3x)/3 < 12/3#

#x < 4#

Now, we need to express *less* than

Since there is no lower bound,

So, the interval is *equal*