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anonymous
 one year ago
Help please..
Write the following inequality in slopeintercept form.
12x  3y ≤ 21
A) y ≤ 4x  7
B) y ≥ 4x  7
C) y ≤ 4x + 7
D) y ≥ 4x + 7
anonymous
 one year ago
Help please.. Write the following inequality in slopeintercept form. 12x  3y ≤ 21 A) y ≤ 4x  7 B) y ≥ 4x  7 C) y ≤ 4x + 7 D) y ≥ 4x + 7

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Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1hint: if I subtract 12x at both sides, I get: \[\Large 12x  3y  12x \leqslant  21  12x\] please simplify

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1no, I get this: \[\Large  3y \leqslant  21  12x\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh 3y and then 2112x= 9?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1then I divide both sides by 3. In doing that our inequality change its direction, because 3 is a negative number. So we can write this: \[\Large y \geqslant \frac{{  21  12x}}{{  3}}\] please simplify again

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so we don't solve for 2112x?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2@proud_yemeniah_ What is 5 books  3 books? You have 5 books and you take away 3 books. What is that equal to?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1are you sure? @proud_yemeniah_

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2It is 2 books. Since 5 books and 3 books are different amounts of the same type of thing (books) you can subtract 3 books from 5 books.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2@proud_yemeniah_ What is 5 books  2 dogs?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Lol u can't subtract dogs from books

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.25 books  2 dogs cannot be simplified further since books and dogs are completely different things. They cannot be combined together, so 5 books  3 dogs is simply 5 books  3 dogs. This is the same with 21 and  21x A plain number like 21 is just a plain number. The term 21x means 21 times x. x is a variable that stands for a number, but we don't know now what number it is. You cannot combine 21 and 12x, just like you cannot combine books and dogs. Just like books and dogs are "unlike terms", so 21 and 12x are unlike terms. Unlike terms cannot be combined together using addition or subtraction.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2You probably have had problems in which you need to combine like terms. Like terms are terms that have exactly the same variables and the same exponents. Those terms can be added and subtracted. Unlike terms, with different variables, cannot be added or subtracted.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh okay, I get it.. it makes sense now

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Great. Let's take your problem from the beginning.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2The slopeintercept form of the equation of a line is: \(\Large y = mx + b\) You were given an inequality, and you are asked to write it in slopeintercept form. That is the same as asking to solve the inequality for y.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2\(\large 12x  3y \le 21\) We want only y on the left side. The first step is to subtract 12x from both sides. This is what @Michele_Laino did above. \(\large 12x 12x  3y \le 12x 21\) We combine like terms on the left side: 12x  12x = 0, so we get: \(\large 3y \le 12x  21\) We can't do anything on the right side since the terms on the right side are unlike terms (remember books and dogs).

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2On the left side we have 3y, but we want just y. Since the 3 is multiplying the y, we need to divide both sides by 3. The rule in an inequality is that when we multiply or divide both sides by a negative number, the inequality sign changes direction. \(\large \dfrac{3y}{3} \ge \dfrac{12x}{3}  \dfrac{21}{3} \)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Now we do all the divisions by 3 being careful with the signs. \(\large y \ge 4x + 7\)
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