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 5128 October 13, 2012
One-step inequalities – Adding and subtracting – Integers – easy 278.6 kB 3356 October 13, 2012
One-step inequalities – Adding and subtracting – Integers – medium 300.5 kB 3436 October 13, 2012
One-step inequalities – Adding and subtracting – Integers – hard 313.4 kB 1711 October 13, 2012
One-step inequalities – Adding and subtracting – Integers – very hard 340.1 kB 1387 October 13, 2012
Adding and subtracting decimals
One-step inequalities – Adding and subtracting – Decimals – easy 309.1 kB 1154 October 13, 2012
One-step inequalities – Adding and subtracting – Decimals – medium 320.9 kB 893 October 13, 2012
One-step inequalities – Adding and subtracting – Decimals – hard 322.4 kB 729 October 13, 2012
One-step inequalities – Adding and subtracting – Decimals – very hard 368.3 kB 643 October 13, 2012
Adding and subtracting fractions
One-step inequalities – Adding and subtracting Fractions – very easy 275.6 kB 1260 October 13, 2012
One-step inequalities – Adding and subtracting – Fractions – easy 321.9 kB 1161 October 13, 2012
One-step inequalities – Adding and subtracting – Fractions – medium 348.1 kB 903 October 13, 2012
One-step inequalities – Adding and subtracting – Fractions – hard 365.7 kB 740 October 13, 2012
One-step inequalities – Adding and subtracting – Fractions – very hard 476.9 kB 657 October 13, 2012
Multiplying and dividing integers
One-step inequalities – Multiplying and dividing – Integers – very easy 290.9 kB 2465 October 13, 2012
One-step inequalities – Multiplying and dividing – Integers – easy 303.5 kB 1941 October 13, 2012
One-step inequalities – Multiplying and dividing – Integers – medium 315.3 kB 2102 October 13, 2012
One-step inequalities – Multiplying and dividing – Integers – hard 330 kB 1127 October 13, 2012
One-step inequalities – Multiplying and dividing – Integers – very hard 377.6 kB 815 October 13, 2012
Multiplying and dividing decimals
One-step inequalities – Multiplying and dividing – Decimals – very easy 349.7 kB 796 October 13, 2012
One-step inequalities – Multiplying and dividing – Decimals – easy 351.3 kB 702 October 13, 2012
One-step inequalities – Multiplying and dividing – Decimals – medium 388.3 kB 690 October 13, 2012
One-step inequalities – Multiplying and dividing – Decimals – hard 412.7 kB 588 October 13, 2012
One-step inequalities – Multiplying and dividing – Decimals – very hard 432.7 kB 548 October 13, 2012
Multiplying and dividing fractions
One-step inequalities – Multiplying and dividing – Fractions – very easy 315.1 kB 888 October 13, 2012
One-step inequalities – Multiplying and dividing – Fractions – easy 323.4 kB 728 October 13, 2012
One-step inequalities – Multiplying and dividing – Fractions – medium 362.7 kB 688 October 13, 2012
One-step inequalities – Multiplying and dividing – Fractions – hard 367 kB 554 October 13, 2012
One-step inequalities – Multiplying and dividing – Fractions – very hard 448.7 kB 571 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 2870 October 14, 2012
One-step inequalities – Adding and subtracting – Decimals 5.4 MB 869 October 14, 2012
One-step inequalities – Adding and subtracting – Fractions 5.3 MB 876 October 14, 2012
One-step inequalities – Multiplying and dividing – Integers 4.6 MB 2084 October 14, 2012
One-step inequalities – Multiplying and dividing – Decimals 5.7 MB 865 October 14, 2012
One-step inequalities – Multiplying and dividing – Fractions 5.3 MB 796 October 14, 2012

 

One-step inequalities knowledge test