Question

Solve graphically : 3x + 4 ≤ 0

Answer 1

Consider the line whose equation is 3x + 4 = 0, i.e. x = `-(4)/(3)`.
This represents a line parallel to Y-axis passing through the point `(-4/3, 0)`.
Draw the line x = `-(4)/(3)`.
To find the solution set, we have to check the position of the origin (0, 0).
When x = 0, 3x + 4 = 3 x 0 + 4 = 4 `cancel<=` 0
∴ the coordinates of the origin does not satisfy thegiven inequality.
∴ the solution set consists of the line x = `-(4)/(3)` the non-origin side of the line which is shaded in the graph.