If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## Get ready for Algebra 1

### Course: Get ready for Algebra 1>Unit 1

Lesson 11: One- and two-step inequalities

# One-step inequalities: -5c ≤ 15

In addition to solving the inequality, we'll graph the solution. Remember to swap if you mutiply both sides of the inequality by a negative number. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• couldn't you just divide both by -5 and get the same answer?
• yeah i see that now, i think u could! but he flipped the sign and i think that means something
(1 vote)
• How could this be used in everyday life?
• When you are trying to find the max profit or minimum scores you need to get in order to get an A. Something like that.
• So why exactly must we flip the signs?
• Think of it this way: if I have -3 x< 9, suppose I do not like to flip inequality signs by dividing by a negative Starting with the equation -3x<9
My other choice is to move my x by opposites
-3x + 3x < 9 + 3x
0< 9 +3x I still do not have x isolated, so I subtract 9
0-9<9-9+3x
-9 < 3x divide by 3
-9/3 < 3/3x
-3 < x if -3 is less than x, then when I flip this equation
x > -3 x must be greater than -3

Starting from beginning -3x < 9 divide by -3 and flip inequality sign
-3/-3x > 9/-3
x > -3

It is easier to remember to flip the inequality sign than to go through the whole process of moving my x to make it positive which makes me move everything else also - the difference between one step and multiple steps

Hope that helps and you understand the inequality flip now
• how did sal get 15 times -1/5 = -3 im confused
• Multiplying by a fraction is the same as dividing by the reciprocal of the fraction. (A reciprocal is the number you get if you switch the numerator and denominator. So, the reciprocal of 2/3 is 3/2 and the reciprocal of 1/5 is 5.)

So, 15 × (-⅕) = 15 ÷ (-5) = -3
• Tip to people watching this video:
• y? 🫥
• can't you just divide instead of using the inverse I've tested this on multiple problems and it seems to work every time? just wondering now instead of figuring out I can't do this down the road once problems become more complicated. Thanks.
• Dividing by -5 and multiplying by -1/5 are exactly the same operation and create the same result.
For example: -5c * -1/5 = -5c/(-5) which is division by -5.
So, use the one you are comfortable with.
• How is -1/5 the reciprocal of -5?
• -5 in fraction form is -5/1
Flip the fraction to get its reciprocal and you have -1/5

Hope this helps.
• Where did the fraction come from?!?!?!?!?!?!?!
• Sal has two ways of changing -5c into just c.
1) Divide both sides by -5
2) Multiply by the reciprocal of -5, which is -1/5

they both achieve the same result. Pick the one you are comfortable with.
Hope this helps.
• what if you multiply a negative number? does the sign flip
• Yes, adding to Allison's answer, because you would technically have to divide by a negative in a case like that. For example in -x/8>10 (I'm going to go step by step -not going straight to multiply each side by -8) Multiply each side by 8 to get -x>80, to isolate x from here, you have to divide by a negative 1, so the sign does switch. Hope this clears up any confusion you have on this
• can't we divide both sides by 5
• You can, but you're left with "-c", not "c". You're solving for "c", not "-c".

Dividing both sides of "-5c ≤ 15" by 5 gives "-c ≤ 3". Perhaps you're uncomfortable with "flipping" the equality.

If you're still uncomfortable with flipping the side then a way to see why.

-c ≤ 3 [ The "-c" expression ]
0 ≤ 3 + c [ Add "c" to both sides ]
-3 ≤ c [ Subtract "-3" from both sides ]

Now the "c" is on the greater than side of the expression.

Flipping the sign is the correct procedure.

I hope this helps.