Solving Inequalities

Solve   

Solve   

Here are two inequalities.

and are integers.

Work out the greatest possible value of

Here is a sketch of the curve   

Work out the values of for which   

Give your answer as an inequality.

is an integer such that 

Find all the possible values of .

Solve the inequality 

Solve 

Represent your solution set to part (a) on the number line below.

Here is a rectangle.

Given that the area of the rectangle is less than

find the range of possible values of .

Solve the inequality 

The diagram shows a rectangle.

The area of the rectangle is 
Given that 
find the range of possible values for 

Martha’s solution to the inequality  is shown on the number line.

Is her solution correct?
Explain your reasoning.

Solve the inequality.

Find the interval for which 

..........................  ..........................

is an integer.

Write down all the possible values of .

Solve    

is an integer such that  

Write down all the possible values of .

Solve   

Solve 

is an integer with 

Write down all the values of

Circle the possible value of .

2.8

3

Solve  

is an integer.

and

Work out all the possible values of .

Solve 

Solve  

Write down the inequality represented by the number line.

Solve  

Here is the graph of  where  is a quadratic function.

Write down all the integer solutions of 

Write down the inequality shown on the number line.

Solve the inequality 

On the number line, show the inequality

is an integer.

Write down all the values of that satisfy

Solve the inequality

On the number line below, represent the solution set of the inequality solved in part (a).

Solve the inequality

Show your working clearly.

Solve the inequality 

Show clear algebraic working.

Solve the inequality 

Solve  .

Show your solution on the number line.

Solve 

Show your solution on the number line.

Gemma’s solution to the inequality 

Is Gemma’s solution correct?
Explain your reasoning.

Solve.