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mathematics UK Year 10 Mathematics (KS4)
 
Solved problems for the chapter:
 

Inequalities and number lines

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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:inequalities_and_number_lines/5317/


Example 1.

Solve the inequality:


    
Example 2.

Solve the systems of inequalities, write the intervals of the solution and present them on a number line.




    
3.

Solve the systems of inequalities, write the intervals of the solution and present them on a number line.




    
4.

Solve the inequality if x is a natural number.


    
5.

Given the equation:




  • Solve the equation.


  • For what values of a are the solutions of the equation positive?

    
6.

Solve the systems of inequalities, write the intervals of the solution and present them on a number line.




    
7.

Draw a point on the number line that represents the number .

    
8.

Given the inequality:




  • Solve the inequality.


  • For which real number a will the inequality be greater than - 2.

    

9.

Draw a point on the number line that represents the number .

    
10.

Given the inequality:




a) Solve the inequality.


b) For what real number a less than 5 solves the inequality.

    
11.

Draw a point on the number line that represents the number .

    
12.

If a and b are the solutions of the system of inequalities:






Find real numbers a and b from the interval

   
13.

Draw a point on the number line that represents the number .

    
14.

Solve for a in the inequalities:


    
15.

Draw a point on the number line that represents the number .

    
16.

Solve for a in the inequalities:


    
17.

Draw a point on the number line that represents the number .

    
18.

Solve for a in the inequalities:


    

19.

Draw a point on the number line that represents the number .

    
20.

Solve for a in the inequalities:


    
21.

Is Andreana right when he says, "On a number line, we always draw the smaller number to the left of the larger one."

    
22.

The inequality is given where


  • Solve for a in the inequality.


  • For what value of a will the interval of the solution be ?

    
23.

Calculate the absolute values ​​of the following numbers:













    
24.

Solve the inequality:


    
25.

Represents the following rational numbers on a number line.


    
26.

Solve the system of inequalities:




    
27.

Solve the systems of inequalities, write the intervals of their solution and present them on a number line.


    
28.

Solve the inequality:


    

29.

Solve the inequality:


    
30.

Solves the inequality in the set of rational numbers.


    
31.

Show graphically, the set of points for which

   
32.

Show graphically, the region for which

   
33.

Show that the lines and intersect on the x-axis.

    
34.

Solve the inequality graphically: