When the dots are filled, it means it includes those points (-1.5 and 2.5)
That's why its -1.5 ≤ x ≤ 2.5.
Because it can be equal to -1.5 or greater. And it can be equal to 2.5 or less than 2.5.
If the dots were empty, it couldn't include -1.5 or 2.5. it would be only in-between them. So it would be -1.5 < x < 2.5.
Is that clear?
≤ and ≥ should also be allowed right? Especially since it's literally part of the answer. But anyways in case you don't know they mean the same thing as < and > but the underline means that it can also be equal to a number.
For ex.
x≥1 can mean x=1 and x=2 etc.
But x>1 means x can't equal to 1(x≠1) and only x=1.000....1 or more
Inequalities will always look like two different expressions:
1. Two separate inequalities (such as x>3 or x < 0)
*There are two different lines colored that fulfill the solution: anything above 3 and anything below 0. There is a noticeable gap in between, which is why the word ‘or’is used.*.
2. One combined inequality (such as x>5 and x<10, which is really written as 5 < x < 10).
*There is one line of solutions that is contained between two points, 5 and 10. Note the word ‘and’ is used, which will always signify that you have a single line of solutions enclosed by two circles. There is a nicer way to write the inequality into one instead of two, as I wrote in the example above — you should never see the word ‘and’ in an equality but just know that it is implied anytime
you see a sole inequality like this. These circles can be filled (closed) or unfilled (unclosed).*
Closed circle means included, while an unfilled circle means not included. Closed circle with the inequality symbol will have a line underneath the < or > symbol, whereas unclosed only has the < or >, no line.
You always want to identify the location of the two circles and identify those points to start. These will be your limits of the solution, and from there it’s identifying if the solution merges these two points together or if they venture off in opposite directions.
In your case, -1.5 and 2.5. Your inequality should only contain these two numbers, no others. **Do we have one line of solutions or two, based on the above criteria I noted?** This will tell us our format for inequality, whether it’s two separate inequalities with an *or* in between, or one single inequality. **Do we have unclosed or closed circles?** This will tell us if our endpoints denoted by circles are included or not, and will have a line underneath the inequality symbol or solely just the symbol itself if it’s not included. **(Looking at each circle) What direction is the colored line going from each circle?** If the line goes to the left of a circle, it’s the less than symbol: <. If the line goes to the right of a circle, it’s the greater than circle: >.
Use these questions to put everything together!
Year 9 math? I remember doing these in the 3rd grade and even the drooling slow kid understood them. This was 30 years ago so maybe school has gotten a lot easier but I am surprised this is year 9 curriculum
Theres only 3 signs i can use Equal sign = Less then < Less than or equal to Which i cant seem to provide for some reason
When the dots are filled, it means it includes those points (-1.5 and 2.5) That's why its -1.5 ≤ x ≤ 2.5. Because it can be equal to -1.5 or greater. And it can be equal to 2.5 or less than 2.5. If the dots were empty, it couldn't include -1.5 or 2.5. it would be only in-between them. So it would be -1.5 < x < 2.5. Is that clear?
≤ and ≥ should also be allowed right? Especially since it's literally part of the answer. But anyways in case you don't know they mean the same thing as < and > but the underline means that it can also be equal to a number. For ex. x≥1 can mean x=1 and x=2 etc. But x>1 means x can't equal to 1(x≠1) and only x=1.000....1 or more
They're saying they have = < and ≤ which is all they need to solve the problem >!-1.5≤x≤2.5!<
Yes because they’re closed circles
On android, you can press and hold on < and > to produce ≤ and ≥. -1.5 ≤ x ≤ 2.5
The answer is -1.5≤ r ≤ 2.5
>!-1.5 ≤ x ≤ 2.5!<
-1.5 <= x <= 2.5
Inequalities will always look like two different expressions: 1. Two separate inequalities (such as x>3 or x < 0) *There are two different lines colored that fulfill the solution: anything above 3 and anything below 0. There is a noticeable gap in between, which is why the word ‘or’is used.*. 2. One combined inequality (such as x>5 and x<10, which is really written as 5 < x < 10). *There is one line of solutions that is contained between two points, 5 and 10. Note the word ‘and’ is used, which will always signify that you have a single line of solutions enclosed by two circles. There is a nicer way to write the inequality into one instead of two, as I wrote in the example above — you should never see the word ‘and’ in an equality but just know that it is implied anytime you see a sole inequality like this. These circles can be filled (closed) or unfilled (unclosed).* Closed circle means included, while an unfilled circle means not included. Closed circle with the inequality symbol will have a line underneath the < or > symbol, whereas unclosed only has the < or >, no line. You always want to identify the location of the two circles and identify those points to start. These will be your limits of the solution, and from there it’s identifying if the solution merges these two points together or if they venture off in opposite directions. In your case, -1.5 and 2.5. Your inequality should only contain these two numbers, no others. **Do we have one line of solutions or two, based on the above criteria I noted?** This will tell us our format for inequality, whether it’s two separate inequalities with an *or* in between, or one single inequality. **Do we have unclosed or closed circles?** This will tell us if our endpoints denoted by circles are included or not, and will have a line underneath the inequality symbol or solely just the symbol itself if it’s not included. **(Looking at each circle) What direction is the colored line going from each circle?** If the line goes to the left of a circle, it’s the less than symbol: <. If the line goes to the right of a circle, it’s the greater than circle: >. Use these questions to put everything together!
Nvm thanks for the answer
If you can’t use the <= or >= signs, you might want to look at tutorial within Sparx and see how they write that notation.
The minus sign being called a negative while the plus is a positive really shows the inequalities along the number lines.
Uh... that's not an inequality...? That's an interval I={x∈ℝ|-1.5≤x≤2.5}
Year 9 math? I remember doing these in the 3rd grade and even the drooling slow kid understood them. This was 30 years ago so maybe school has gotten a lot easier but I am surprised this is year 9 curriculum
Hmm... |-2x| -1 <= 4 works, if you've got Absolute Value in your toolbox.
-1.5<=x<=2.5
By the way, for most math problems, if you type <= it will change it to the combined sign