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Course: Algebra basics>Unit 3

Lesson 4: One-step inequalities

One-step inequalities review

Review evaluating one-step inequalities, and try some practice problems.

Inequalities symbols

SymbolMeaning
$>$Greater than
$\underset{―}{>}$Greater than or equal to
$<$Less than
$\underset{―}{<}$Less than or equal to

Evaluating inequalities with addition and subtraction

We evaluate inequalities like we evaluate equations: we want to isolate the variable.
Example 1: $x+7>4$
To isolate $x$, let's from both sides.
$x+7-7>4-7$
Now, we simplify.
$x>-3$
Example 2:
To isolate $z$, let's to both sides.
Now, we simplify.
Want to learn more about one-step inequalities? Check out this video.

Practice set 1

Problem 1A
Solve for $x$.
Your answer must be simplified.
$x-8<-1$

Evaluating inequalities with multiplication and division

Again, we want to isolate the variable. But things will get a little different when multiply or divide by a negative number. Look carefully to see what happens!
Example 1: $10x<-3$
To isolate $x$, let's divide both sides by $10$.
$\frac{10x}{10}<\frac{-3}{10}$
Now, we simplify.
$x<-\frac{3}{10}$
Example 2:
To isolate $y$, let's multiply both sides by $-6$.
Now, we simplify.

Practice set 2

Problem 2A
Solve for $x$.
Your answer must be simplified.
$2x<15$

Want to try more problems like this? Check out this exercise.

Want to join the conversation?

• How am I suppose to know when to flip the inequality if you re suppose to
(23 votes)
• You are supposed to flip an inequality when you multiply or divide either side by a negative number. You do this because when multiplying sides by a negative number, you change the sign of each side, making the previously greater side less.
(55 votes)
• Math needs to solve its own problems. I'm not a life expert!
(31 votes)
• i fully agree with łogic
(2 votes)
• How can anyone do this.
(24 votes)
• it is confusing but it takes practice
(0 votes)
• I keep getting confused on when to switch or not
(16 votes)
• me to.
I keep forgetting.
(3 votes)
• I'm having trouble with entering data & answers in "One-step inequalities" Review. First, I can not enter my answers because the POP-UP icons won't clear. Specifically, the problem "2x<15". At the present, the entire Exercise "One-Step Inequalities Review" is LOCKED-UP. Please Help. Henry
(11 votes)
• Just click the screen to the left, right, top, or bottom of the pop-up. It should clear just fine. If it doesn't, sorry, maybe your device has a glitch.
(6 votes)
• This math aint' mathin' and my brain aint' brainin'
(13 votes)
• this is just pre algebra
you probably understand by now
(0 votes)
• i kind of get it but still to hard for me.
(7 votes)
• if you want to add or subtract you have to put the x alone example: h+3<8
you will subtract the 2 sides by 3
h+3<8
-3 -3
h<5
and that is your answer.

same goes for multiplting and dividing but it has only one diffrent rule in -/+ you never change the sign but in x/dividing when ever you multiply or divid with a negative number you must change the sign
example: -5h>20 when you see a number stuck to a varibale than you must now that there is a hiden multipication sign so what is the opposit of the multipication. division so, -5 divided by 20 is -0.25
and dont forget when ever you multiply of divide by a negative number you change the inequality sign.
the answer will be h<-0.25
(11 votes)
• this is not the way my teacher teached me
(9 votes)
• Can someone help me i get confused when it comes to switch the sign do you flip it when it has a negative in the problem or do you flip the sign when is a negative.
(7 votes)
• we have to change the symbols when he have a negative number?
(4 votes)
• We reverse the inequality only if we multiply or divide both sides of the inequality by a negative number.
Hope this helps.
(9 votes)
• For the last question in the second exercise, problem 2c, can we not equally put x is less than or equal to 3 1/3?
(8 votes)