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Inequalities for SQA Higher Maths

Inequalities

This page covers the following topics:

1. Quadratic inequalities

To solve quadratic inequalities, rearrange them so that one side is 0. Then solve the corresponding quadratic equation. Sketch the graph of the quadratic equation using the roots and deduce the range of values the variable can take. When the quadratic expression is greater than 0, the wanted region is above the x-axis, and when the quadratic expression is less than 0, the wanted region is below the x-axis.

Quadratic inequalities

1

What is the set of values of x for which 4(xยฒ โˆ’ 2x) โ‰ค x(5 + 2x) + 7?

[โˆ’0.5, 7]

What is the set of values of x for which 4(xยฒ โˆ’ 2x) โ‰ค x(5 + 2x) + 7?

2

A painter wants to make a painting of sides x โˆ’ 7 and x โˆ’ 11. Given that he wants the area of the painting to be at least 12 unitsยฒ, find the range of possible values of x.

image

A painter wants to make a painting of sides x โˆ’ 7 and x โˆ’ 11. Given that he wants the area of the painting to be at least 12 unitsยฒ, find the range of possible values of x.

3

Solve 7(11 + x โˆ’ xยฒ) โ‰ค 5(x โˆ’ xยฒ) โˆ’ x.

image

Solve 7(11 + x โˆ’ xยฒ) โ‰ค 5(x โˆ’ xยฒ) โˆ’ x.

4

Find the range of possible values of x for 3/x โˆ’ 8 โ‰ค 4.

image

Find the range of possible values of x for 3/x โˆ’ 8 โ‰ค 4.

5

What is the set of values of x for which x(14 โˆ’ x) โ‰ฅ 33?

image

What is the set of values of x for which x(14 โˆ’ x) โ‰ฅ 33?

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