Question

solution to the inequality
`5x+7y>-3

Answer 1

To solve the inequality 5x + 7y > -3, we can follow these steps:

Step 1: Solve the equation 5x + 7y = -3 for y:
5x + 7y = -3
7y = -3 - 5x
y = (-3 - 5x) / 7

Step 2: Represent the inequality as a graph:
y > (-3 - 5x) / 7

Step 3: Graph the line y = (-3 - 5x) / 7 as a dotted line since it is a strict inequality.

Step 4: Choose a point on either side of the line (not on the line) and shade that side of the line to represent the solution region. If (0, 0) is chosen, substitute the x and y values into the inequality:
5(0) + 7(0) > -3
0 > -3

Since 0 is greater than -3, the side containing the point (0, 0) is the solution region.

Therefore, the solution to the inequality 5x + 7y > -3 is the region above the line y = (-3 - 5x) / 7.