Question

review
determine whether the given points are solutions to the
≤ 16 \t\t\t\t\t\t\t y + 6 > 3(x - 1)
(there are grids, tables with points (-3,3), (-1,4), (0,0), (0,-9), (3,3) and columns yes and no for solution determination)

Explanation:

To determine if a point \((x, y)\) is a solution to the inequality \(y + 6>3(x - 1)\), we substitute the \(x\) and \(y\) values of the point into the inequality and check if the inequality holds true.

Step 1: For the point \((-3, 3)\)

Substitute \(x=-3\) and \(y = 3\) into the inequality \(y+6>3(x - 1)\)
Left - hand side (LHS): \(y + 6=3 + 6=9\)
Right - hand side (RHS): \(3(x - 1)=3\times(-3-1)=3\times(-4)=- 12\)
Since \(9>-12\), the inequality holds. So \((-3,3)\) is a solution (Yes).

Step 2: For the point \((-1, 4)\)

Substitute \(x=-1\) and \(y = 4\) into the inequality \(y + 6>3(x - 1)\)
LHS: \(y + 6=4 + 6 = 10\)
RHS: \(3(x - 1)=3\times(-1 - 1)=3\times(-2)=-6\)
Since \(10>-6\), the inequality holds. So \((-1,4)\) is a solution (Yes).

Step 3: For the point \((0, 0)\)

Substitute \(x = 0\) and \(y=0\) into the inequality \(y + 6>3(x - 1)\)
LHS: \(y + 6=0+6 = 6\)
RHS: \(3(x - 1)=3\times(0 - 1)=3\times(-1)=-3\)
Since \(6>-3\), the inequality holds. So \((0,0)\) is a solution (Yes).

Step 4: For the point \((0,-9)\)

Substitute \(x = 0\) and \(y=-9\) into the inequality \(y + 6>3(x - 1)\)
LHS: \(y + 6=-9 + 6=-3\)
RHS: \(3(x - 1)=3\times(0 - 1)=-3\)
The inequality is \(y + 6>3(x - 1)\), and \(-3\) is not greater than \(-3\) (it is equal). So the inequality does not hold. Thus, \((0,-9)\) is not a solution (No).

Step 5: For the point \((3, 3)\)

Substitute \(x = 3\) and \(y = 3\) into the inequality \(y + 6>3(x - 1)\)
LHS: \(y + 6=3+6 = 9\)
RHS: \(3(x - 1)=3\times(3 - 1)=3\times2 = 6\)
Since \(9>6\), the inequality holds. So \((3,3)\) is a solution (Yes).

Answer:

For the point \((-3,3)\): Yes
For the point \((-1,4)\): Yes
For the point \((0,0)\): Yes
For the point \((0,-9)\): No
For the point \((3,3)\): Yes