+912 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
+9481 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
