Read each straight boundary separately. Find its equation from coordinates or intercepts, determine whether the boundary is included, then choose the inequality that contains the stated region. Example A region lies above y=2x-1, on or below y=5, and to the right of x=0. If all three boundaries are solid, its inequalities are y 2x-1, y 5, x 0. Test an interior point, such as (1,3), in all three inequalities. If the sloping boundary were broken, replace its >= by >. The picture alone does not make an excluded boundary inclusive.

Read each straight boundary separately. Find its equation from coordinates or intercepts, determine whether the boundary is included, then choose the inequality that contains the stated region.

A region lies above \(y=2x-1\), on or below \(y=5\), and to the right of \(x=0\). If all three boundaries are solid, its inequalities are \(y\ge2x-1,\ y\le5,\ x\ge0\).

Test an interior point, such as \((1,3)\), in all three inequalities. If the sloping boundary were broken, replace its \(\ge\) by \(>\). The picture alone does not make an excluded boundary inclusive.

Linear Equations and Inequalities

Cambridge IGCSE Mathematics 0580. Initial catalogue covers the assessed demands of February/March 2026 Paper 22; further Core and Extended mappings require paper-level scope review.

Writing inequalities from a region

Writing inequalities from a region