The correct rows in the inequalities are
The rows are given as:
-3x - 4 < x + 4 ⇒ -3x < x
2(x - 5) + 1 ≤ 5 ⇒ 2(x - 5) ≤ 4
-4x ≥ -24 ⇒ x ≤ 6
x = 2y and 2x + 2y > 60 ⇒ 6y > 60
y + 2 ≤ 4 - x and 4 - x ≤ 3y ⇒ y + 2 ≤ 3y
To determine the correct rows, we simply solve each inequality.
This is done as follows:
-3x - 4 < x + 4
Collect like terms
-3x - x < 4 + 4
Evaluate the like terms
-4x < 8
Divide by -4
x > -2
This means that:
-3x - 4 < x + 4 ⇒ -3x < x is false.
2(x - 5) + 1 ≤ 5
Subtract 1 from both sides
2(x - 5) ≤ 4
This means that:
2(x - 5) + 1 ≤ 5 ⇒ 2(x - 5) ≤ 4 is true.
-4x ≥ -24
Divide through by -4
x ≤ 6
This means that:
-4x ≥ -24 ⇒ x ≤ 6 is true.
x = 2y and 2x + 2y > 60
Substitute 2y or x in 2x + 2y > 60
2(2y) + 2y > 60
Evaluate the product
4y + 2y > 60
Evaluate the like terms
6y > 60
This means that:
x = 2y and 2x + 2y > 60 ⇒ 6y > 60 is true.
y + 2 ≤ 4 - x and 4 - x ≤ 3y
We have:
y + 2 ≤ 4 - x and 4 - x ≤ 3y
This can be rewritten as:
y + 2 ≤ 3y
This means that:
y + 2 ≤ 4 - x and 4 - x ≤ 3y ⇒ y + 2 ≤ 3y is true
Hence, the correct rows are 2, 3, 4 and 5
Read more about inequality at:
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