What are the integer solutions to the inequality below?

Mathematics

1 answer:

Dmitry [639]2 years ago

5 0

3 < 3x - 3 ≤ 2x + 2

Adding -3 to each side gives

0 < 3x - 6 ≤ 2x - 1

The left inequality says

0 < 3x - 6 ⇒ 3x > 6 ⇒ x > 2

while the right inequality says

3x - 6 ≤ 2x - 1 ⇒ x ≤ 5

Then the solutions belong to the interval 2 < x ≤ 5 and contains only the integers x = 3, x = 4, and x = 5.

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I need help solving a system of linear equation, and it says to solve it by Substitution.

olga_2 [115]

2x - 3y = -24
x+ 6y = 18

you solve the first one by the x:

2x = -24 + 3y

x = (-24+3y)/2

then you substitute what you found in the other equation and you solve by y

(-24+3y)/2 + 6y = 18 multiply everything by 2

-24 + 3y + 12y = 36

3y + 12y = 36 + 24

15y = 60

y = 60/15

y = 4

Good job! You found your y! :D

Now let's substitute the y in the first equation with 4:

2x - 3(4) = -24

2x - 12 = -24

2x = -24 + 12

2x = -12

x = -12/2

x= -6

Done!! ;)

6 0

3 years ago

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kupik [55]

Answer:

1. 7

Step-by-step explanation:

4 0

3 years ago

Clara found the product of 3 – 6y2 and y2 + 2. Her work is shown below. (3 – 6y2)(y2 + 2) = 3(y2) + (–6y2)(2) = 3y2 – 12y2

Marizza181 [45]