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

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)