Questions on understanding inequality notation and solving inequalities

Solving an inequality of the form ax+b < c where a is negative.

Solving an inequality of the form ax+b < c where a is negative.

Solving an inequality of the form ax+b < c

Solving an inequality of the form ax+b < c

Solving an inequality of the form x/a < b

Solving an inequality of the form ax < b

Solving an inequality of the form x+a < b

Identify the truth value of an inequality (T/F) between two numbers

Identify the truth value of an inequality (T/F) between two numbers

Inequality involving a single absolute value, question solution uses the piecewise nature of the absolute value function.

Given one or two circles centre (0,0) describe the region given by the circle inequality ( or inequalitites). e.g. x^2+y^2 < 4

Given a circle centre and radius, write an appropriate inequality for the region either inside or outside the circle.

Draw the annulus given by a double inequality. The user moves circles on an interactive jsxgraph.

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In parts (a) and (b) rearrange linear inequalities to make $x$ the subject.

In the parts (c) and (d) correctly give the direction of the inequality sign after rearranging an inequality.

Identify the truth value of an inequality (T/F) between two numbers

Identify the truth value of an inequality (T/F) between two numbers

Identify the truth value of an inequality (T/F) between two numbers

Identify the truth value of an inequality (T/F) between two numbers

Finding element of a set, requires knowledge of inequality and notation for integer and real number.

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Inequality involving a single absolute value, question solution uses the piecewise nature of the absolute value function.

Inequality involving a single absolute value, question solution uses the piecewise nature of the absolute value function.

This question applies a rewriting rule to the student's answer and correct answer, to interpret chained inequalities $a<b<c$ and $a>b>c$ as $(a<b) \wedge (b<c)$ and $(a>b) \wedge (b>c)$ respectively.

This is a work-around until the parser interprets chained relations this way automatically.

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Question on $\displaystyle{\lim_{n\to \infty} a^{1/n}=1}$. Find least integer $N$ s.t.  $\ \left |1-\left(\frac{1}{c}\right)^{b/n}\right| \le10^{-r},\;n \geq N$

Let $x_n=\frac{an+b}{cn+d},\;\;n=1,\;2\ldots$. Find  $\lim_{x \to\infty} x_n=L$ and find least $N$ such that $|x_n-L| \le 10^{-r},\;n \geq N,\;r \in \{2,\;3,\;4\}$.

In the first three parts, rearrange linear inequalities to make $x$ the subject.

In the last four parts, correctly give the direction of the inequality sign after rearranging an inequality.

This question takes the student through variety of examples of quadratic inequalities by asking them for the range(s) for which $x$ meets the inequality.