Algebra Question sentence with or?

Question

negative 3 < 2y+9 or 18> 4y - 10

Answer 1

"OR" means that if either is true then the statement is true. It is the same as "union" in set theory.

-3<2y + 9 OR 18>4y - 10

-12<2y OR 28>4y

6>2y OR 7>y

3>y or 7>y

The more inclusive statement is 7>y (same as y<7).

Answer 2

negative 3 < 2y+9 or 18> 4y - 10

Is this

-3 < 2y+9 or 18> 4y - 10

Are these two inequalities that you want solved?


-3 < 2y+9

Solve as you would an equation. When you multiply or divide by a negative number remember to reverse the sense.

-3 < 2y+9

Add -9 to both sides
-12 < 2y

Divide both sides by 2
-6 < y

I can put the y on the left side but I do not change the sense! The y is greater before and still greater after.

[ y > -6 ]



18> 4y - 10

Add 10 to both sides
28 > 4y

Divide both sides by 4
7 > y

Move the y to the left side without changing the sense.
[ y < 7 ]

-6 < y < 7

Answer 3

-3 < 2y + 9
-3 - 9 < 2y
-12 < 2y
-6 < y

18 > 4y - 10
18 + 10 > 4y
28 > 4y
7 > y

If we put these two results together, we get -6 < y < 7.

We can write the result this way because the inequality can also be read from right to left. Reading it that way we get 7 is greater than y, which is greater than -6. That solution satisfies both inequalities because if we plug any value for y between -6 and 7 into either one of these inequalities the result is a true statement.

Answer 4

- 3 < 2y+9 or 18> 4y - 10

the value of y is between (or)
assume that
-3 < 2y + 9 ,but final ans. y should be smallest than -3
so y cannot be -6 , y = -5 or y = -11/2
-3 < 2(-6) + 9 = -3 < -3 ...wrong
-3 < 2(-5) + 9 = -3 < -1 ...correct

18> 4y - 10
so y cannot be 7 , y = 6 or y = 13/2
18> 4(7) - 10 = 18 > 18 ...wrong
18> 4(6) - 10 = 18 > 14 ...correct


y can be any number between -6 and 7, but cannot be -6 and 7!
-6 < y < 7....................

Answer 5

Solve the first one by adding -9 to both sides and then dividing by 2, you get -6 < y.
For the second, add 10 to both sides and divide by 4, thus
7 > y which is the same as y < 7.

If you look at both these sets on the number line, i.e. all the numbers to the right of -6, and all the numbers to the left of 7, you see that together they cover the whole line. So if it's "or", that means y can be any value in the first one or any value in the second (including those numbers in both), so it's ALL REAL NUMBERS.

Sorry, I didn't notice the word "negative" in your question at first, and have now corrected my solution.

If it had been "and", then the only values of y in the solution would be those satisfying both sentences, i.e. the numbers which are greater than -6 and also less than 7, so we would write
-6 < y < 7

I notice a couple of other answerers have done correct mechanical work in solving these statements, but have not dealt with the fact that you said they are "or" statements. Please note my explanation above. The fact is that any real value of y will satisfy one of the statements, and values between -6 and 7 will satisfy both.

Answer 6

so relatively, you have 40 two.6 grams of cereal, and you already know that for each 28.4 grams of cereal, it consists of a hundred and ten energy. what you prefer to do is to get a ratio of the quantity of cereals you certainly have, then multiply it by means of a hundred and ten energy. So in mathematic words, you get 40 two.6/28.4, you ought to get a ratio of one million.5, this ability that the quantity of cereal you have is one million.5 cases extra advantageous than 28.4 grams, as a results of fact you already know that for each 28.4 grams of cereal you will get a hundred and ten energy, so which you purely multiply a hundred and ten energy by means of one million.5 to get the excellent energy..it relatively is a hundred sixty five energy. wish it facilitates

Answer 7

2y>-6
y>-3
18>4y
18/4>y
18/4>y>-3