Drag each inequality to the column which is labeled with its solution.
x 4
2(x + 6) < 3x + 8
3(x – 5) + x x
2(x + 8) > 4x + 2
Drag each inequality to the column which is labeled with its solution. x 4 2(x + 6) < 3x + 8 3(x – 5) + x x 2(x + 8) > 4x + 2
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To solve the inequalities and place them in the correct solution column, let’s analyze each one step by step.
1. For the first inequality:
[ 2(x + 6) < 3x + 8 ]
Expanding gives us:
[ 2x + 12 < 3x + 8 ]
Rearranging leads to:
[ 12 – 8 < 3x - 2x ]
Which simplifies to:
[ 4 < x ]
or
[ x > 4 ]
2. For the second inequality:
[ 3(x – 5) + x < x ]
Expanding gives us:
[ 3x – 15 + x < x ]
Rearranging leads to:
[ 4x – 15 < x ]
Subtracting (x) from both sides gives:
[ 4x – x – 15 < 0 ]
Simplifying gives:
[ 3x – 15 < 0 ]
or
[ 3x < 15 ]
so
[ x < 5 ]
3. For the third inequality:
[ 2(x + 8)