One-step inequalities

One-step inequalities are very easy to solve. They are very similar to one-step equations when it comes to the solving procedure. The biggest difference is that, while the solution of an equation is one number, the solution of an inequality is often a large group of numbers. For instance, let us say you have to solve an inequality that looks like this:

x + 4 > 8

The first thing  you have to do is to move the number 4 to the right side of the inequality. Do not forget to change the sign of the number you are moving to the other side. After that, just perform the subtraction. Like this:

x > 8 – 4

x > 4

As you can see, the inequation states that x is greater than 4. That means that the solution of the inequation are all numbers greater than 4.

one step inequalities

Also, a very important thing to remember is to change the sign of inequality when multiplying or dividing the whole expression with a negative number. For example, let us say we have an expression that looks like this:

-4x >16

To get to the value of x, we have to divide the whole expression with (-4). Like this:

-4x > 16 |: (-4)

Now we have to change that sign, or else we will get the wrong result. The final result will be:

x < -4

You can check that result by inserting any value smaller than (-4) as the value of x. If you wish to practice solving one-step inequalities, feel free to use the free math worksheets below.

One-step inequalities exams for teachers

Exam Name File Size Downloads Upload date
Adding and subtracting integers
One-step inequalities – Adding and subtracting – Integers – very easy 271.3 kB 4809 October 13, 2012
One-step inequalities – Adding and subtracting – Integers – easy 278.6 kB 3152 October 13, 2012
One-step inequalities – Adding and subtracting – Integers – medium 300.5 kB 3212 October 13, 2012
One-step inequalities – Adding and subtracting – Integers – hard 313.4 kB 1571 October 13, 2012
One-step inequalities – Adding and subtracting – Integers – very hard 340.1 kB 1291 October 13, 2012
Adding and subtracting decimals
One-step inequalities – Adding and subtracting – Decimals – easy 309.1 kB 1076 October 13, 2012
One-step inequalities – Adding and subtracting – Decimals – medium 320.9 kB 830 October 13, 2012
One-step inequalities – Adding and subtracting – Decimals – hard 322.4 kB 671 October 13, 2012
One-step inequalities – Adding and subtracting – Decimals – very hard 368.3 kB 595 October 13, 2012
Adding and subtracting fractions
One-step inequalities – Adding and subtracting Fractions – very easy 275.6 kB 1174 October 13, 2012
One-step inequalities – Adding and subtracting – Fractions – easy 321.9 kB 1068 October 13, 2012
One-step inequalities – Adding and subtracting – Fractions – medium 348.1 kB 838 October 13, 2012
One-step inequalities – Adding and subtracting – Fractions – hard 365.7 kB 681 October 13, 2012
One-step inequalities – Adding and subtracting – Fractions – very hard 476.9 kB 605 October 13, 2012
Multiplying and dividing integers
One-step inequalities – Multiplying and dividing – Integers – very easy 290.9 kB 2290 October 13, 2012
One-step inequalities – Multiplying and dividing – Integers – easy 303.5 kB 1781 October 13, 2012
One-step inequalities – Multiplying and dividing – Integers – medium 315.3 kB 1938 October 13, 2012
One-step inequalities – Multiplying and dividing – Integers – hard 330 kB 1017 October 13, 2012
One-step inequalities – Multiplying and dividing – Integers – very hard 377.6 kB 744 October 13, 2012
Multiplying and dividing decimals
One-step inequalities – Multiplying and dividing – Decimals – very easy 349.7 kB 738 October 13, 2012
One-step inequalities – Multiplying and dividing – Decimals – easy 351.3 kB 649 October 13, 2012
One-step inequalities – Multiplying and dividing – Decimals – medium 388.3 kB 633 October 13, 2012
One-step inequalities – Multiplying and dividing – Decimals – hard 412.7 kB 545 October 13, 2012
One-step inequalities – Multiplying and dividing – Decimals – very hard 432.7 kB 509 October 13, 2012
Multiplying and dividing fractions
One-step inequalities – Multiplying and dividing – Fractions – very easy 315.1 kB 829 October 13, 2012
One-step inequalities – Multiplying and dividing – Fractions – easy 323.4 kB 664 October 13, 2012
One-step inequalities – Multiplying and dividing – Fractions – medium 362.7 kB 640 October 13, 2012
One-step inequalities – Multiplying and dividing – Fractions – hard 367 kB 512 October 13, 2012
One-step inequalities – Multiplying and dividing – Fractions – very hard 448.7 kB 526 October 13, 2012

 

One-step inequalities worksheets for students

Worksheet Name File Size Downloads Upload date
One-step inequalities – Adding and subtracting – Integers 4.9 MB 2683 October 14, 2012
One-step inequalities – Adding and subtracting – Decimals 5.4 MB 806 October 14, 2012
One-step inequalities – Adding and subtracting – Fractions 5.3 MB 801 October 14, 2012
One-step inequalities – Multiplying and dividing – Integers 4.6 MB 1940 October 14, 2012
One-step inequalities – Multiplying and dividing – Decimals 5.7 MB 803 October 14, 2012
One-step inequalities – Multiplying and dividing – Fractions 5.3 MB 730 October 14, 2012

 

One-step inequalities knowledge test