IGCSEMathsCambridge (CIE)ExtendedFlashcardsCoordinate Geometry & GraphsSolving & Graphing Inequalities

Solving & Graphing Inequalities (Cambridge (CIE) IGCSE Maths)

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FrontRepresenting Inequalities as Regions
True or False?
A solid line is used when drawing the line for the inequality $y \leq x + 1$ .

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Cards in this collection (5)

True or False?
A solid line is used when drawing the line for the inequality $y \leq x + 1$ .
True.
A solid line is used when drawing the line for the inequality $y \leq x + 1$ .
Solid lines are used when the inequality includes an equals, ≤ or ≥.
Which side of the line $x = 1$ satisfies the inequality $x \leq 1$ ?
The side to the left of the line $x = 1$ (including the line itself) satisfies the inequality $x \leq 1$ .
True or False?
The region below the line $y = x - 2$ satisfies the inequality $y > x - 2$ .
False.
The region below the line $y = x - 2$ does not satisfy the inequality $y > x - 2$ .
The region above the line satisfies the inequality.
How could you use the point $(0, 0)$ to determine which side of the line $2 x + 3 y = 12$ satisfies the inequality $2 x + 3 y > 12$ ?
To use the point $(0, 0)$ to determine which side of the line $2 x + 3 y = 12$ satisfies the inequality $2 x + 3 y > 12$ :
- Substitute $x = 0$ and $y = 0$ into $2 x + 3 y$ .
- If the answer is greater than 12 then the side of the line containing $(0, 0)$ satisfies the inequality.
- If the answer is less than 12 then the side of the line which does not contain $(0, 0)$ satisfies the inequality.
How can you identify the inequalities needed to define a region from a graph?
To identify the inequalities needed to define a region from a graph:
- Identify the equation of each line.
- Substitute the coordinates of a point within the region into each equation.
  If the answer is less than the given value in the equation, then it satisfies the inequality $<$ (if the line is dotted) or $\leq$ (if the line is solid)
  If the answer is greater than the given value in the equation, then it satisfies the inequality $>$ (if the line is dotted) or $\geq$ (if the line is solid)

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