**1. Solve for x.**

**−9 < 4x + 3 ≤ 27**

**Enter your answer, as one inequality, in the box.**

**2. Solve for x.**

**7x −9 < 12 or 1/4x + 8 > 11**

Enter your answer, including the **inequality symbol,** in the boxes.

x ______ or x _______

3. **Henrietta is planting a new flower garden. She must have yellow and red rosebushes. Let x represent the number of yellow rosebushes and y represent the number of red rosebushes. She wants at least 4 times as many yellow rosebushes as red rosebushes. Each yellow rosebush costs $7.50 and each red rosebush costs $4.75. She can spend no more than $125.**

**Select all of the constraints for this situation.**

x≥4y

y>0

x>0

7.50x+4.75y≥125

y≥4x

7.50x+4.75y≤125

AngelRay
Dec 16, 2017

#1**0 **

**1.**

-9 < 4x + 3 ≤ 27

We can decrease each part by 3 and still keep the inequality true.

-12 < 4x ≤ 24

Now we can divide through by 4 .

-3 < x ≤ 6

**2.**

7x − 9 < 12 Add 9 to both sides.

7x < 21 Divide both sides by 7 .

x < 3

or

1/4x + 8 > 11 Add 8 to both sides.

1/4x > 19 Multiply both sides by 4 .

x > 76

So... x < 3 or x > 76

**3.**

She wants at least 4 times as many yellow rosebushes as red rosebushes. So...

the number of red bushes is greater than or equal to 4 times the number of yellow bushes.

y ≥ 4x

She can spend no more than $125. So...

the total cost of the yellow bushes + the total cost of the red bushes is less than or equal to $125.

7.50x + 4.75y ≤ 125

Also...she can't buy a negative number of bushes....and she must have each type....so

x > 0 and

y > 0

hectictar
Dec 16, 2017