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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
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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

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