Question
Solve graphically :3x + 4 ≤ 0
✓
Answer
Consider the line whose equation is 3x + 4 = 0,
i.e. $x=-\frac{4}{3}$
This represents a line parallel to $Y$-axis passing through the point $\left(-\frac{4}{3}, 0\right)$.
Draw the line $x=-\frac{4}{3}$.
To find the solution set, we have to check the position of the origin (0, 0). When x = 0, 3x + 4 = 3 × 0 + 4= 4 ≰ 0 ∴ the coordinates of the origin does not satisfy the given inequality.
$\therefore$ the solution set consists of the line $x=-\frac{4}{3}$ and the non-origin side of the line which is
shaded in the graph.
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