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

1. Michele_Laino

hint: if I subtract 12x at both sides, I get: $\Large 12x - 3y - 12x \leqslant - 21 - 12x$ please simplify

2. anonymous

3y & -9

3. Michele_Laino

no, I get this: $\Large - 3y \leqslant - 21 - 12x$

4. anonymous

Oh -3y and then 21-12x= -9?

5. Michele_Laino

then 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

6. anonymous

so we don't solve for -21-12x?

7. mathstudent55

@proud_yemeniah_ What is 5 books - 3 books? You have 5 books and you take away 3 books. What is that equal to?

8. anonymous

2

9. Michele_Laino

are you sure? @proud_yemeniah_

10. mathstudent55

It 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.

11. mathstudent55

@proud_yemeniah_ What is 5 books - 2 dogs?

12. anonymous

Lol u can't subtract dogs from books

13. mathstudent55

5 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.

14. mathstudent55

You 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.

15. anonymous

Oh okay, I get it.. it makes sense now

16. mathstudent55

Great. Let's take your problem from the beginning.

17. mathstudent55

The slope-intercept 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 slope-intercept form. That is the same as asking to solve the inequality for y.

18. mathstudent55

$$\large 12x - 3y \le -21$$ 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).

19. mathstudent55

On 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. $$\large \dfrac{-3y}{-3} \ge \dfrac{-12x}{-3} - \dfrac{21}{-3}$$

20. mathstudent55

Now we do all the divisions by -3 being careful with the signs. $$\large y \ge 4x + 7$$