# How do you solve #10x-6<=4x+42# and graph the solution on a number line?

##### 2 Answers

#### Explanation:

First, subtract

#10x - 6 - color(blue)(4x) le 4x + 42 - color(blue)(4x)#

#6x - 6 le cancel(4x) + 42 - cancel(color(blue)(4x)#

#6x - 6 le 42#

Next, add 6 to both sides.

#6x - 6 + color(red)6 le 42 + color(red)6#

#6x - cancel6 + cancelcolor(red)6 le 48#

#6x le 48#

Finally, divide both sides by 6.

#(6x)/color(limegreen)6 le 48/color(limegreen)6#

#(cancel6x)/cancelcolor(limegreen)6 le 8#

#x le 8#

This is the solution! To graph it on a number line, first consider what the solution is telling you: "x is less than or equal to 8"

We need to include 8 in our solution, and everything less than 8. Therefore, we will draw a solid dot at

*Final Answer*

See a solution process below:

#### Explanation:

First, add

Now, divide each side of the inequality by

To graph this we draw a solid circle at **"or equal to"** clause.

We will draw an arrow to the left of **"less than"** clause: